Question 11 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: If a number is divisible by $3$ and $7$, it must be divisible by $21.$
AnswerTrue.
If a number is divisible by $3$ and $7$, it must be divisible by $21$.
Example: $42$ is divisible by both $3$ and $7$. It is also divisible by $21$.
View full question & answer→Question 21 Mark
Write down all the factors of: $20$
Answer$20 = 1, 2, 4, 5, 10, 20$
View full question & answer→Question 31 Mark
Write $'T'$ for true and $'F'$ for false statement. The $HCF$ of two given numbers is always a factor is their $LCM.$
AnswerTrue.
For example, $4$ and $6$ are two numbers whose $HCF$ is $2$ and $LCM$ is $12$, but $2$ is a factor of $12.$
View full question & answer→Question 41 Mark
Test the divisibility of the following numbers by $3:$
$872645$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$872645$ is not divisible by $3$ because the sum of its digits, $8 + 7 + 2 + 6 + 4 + 5,$ is $32$, which is not divisible by $3$.
View full question & answer→Question 51 Mark
Test the divisibility of the following numbers by $10: 55555$
AnswerA number is divisible by $10$ if its ones digit is $0. 55555$ is not divisible by $10$, because its ones digit is $5,$ not $0$.
View full question & answer→Question 61 Mark
Test the divisibility of the following numbers by $4: 810524$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4$.
$810524$ is divisible by $4$ because the number formed by its tens and ones digits is $24$, which is divisible by $4$.
View full question & answer→Question 71 Mark
Write all the prime numbers between: $80$ and $100$
Answer$80$ and $100 = 83, 89, 97$
View full question & answer→Question 81 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: If a number divides two numbers exactly, it must divide their sum exactly.
AnswerTrue.
If a number divides two numbers exactly, it must divide their sum exactly.
Example: $42$ and $56$ are exactly divisible by $7.$ $42 + 56 = 98,$ which is exactly divisible by $7$.
View full question & answer→Question 91 Mark
Write all the prime numbers between:
$40$ and $80$
Answer$40$ and $80 = 41, 43, 47, 53, 59, 61, 67, 71, 73, 79$
View full question & answer→Question 101 Mark
Write down all the factors of: $60$
Answer$60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$
View full question & answer→Question 111 Mark
Test the divisibility of the following numbers by $10: 5790$
AnswerA number is divisible by $10$ if its ones digit is $0. 5790$ is divisible by $10,$ because its ones digit is $0$.
View full question & answer→Question 121 Mark
Test the divisibility of the following numbers by $2$:
$59628$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$.
Since the digit in the ones place in $59628$ is $8$, it is divisible by $2$.
View full question & answer→Question 131 Mark
Test the divisibility of the following numbers by $9: 3333$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$.
$3333$ is not divisible by $9$, because the sum of its digits, $3 + 3 + 3 + 3,$ is $12,$ which is not divisible by $9$.
View full question & answer→Question 141 Mark
Which of the following statements are true?
The sum of two prime numbers is always a prime number.
AnswerFalse.
$3$ and $7$ are two prime numbers and their sum is $10$, which is even.
View full question & answer→Question 151 Mark
Test the divisibility of the following numbers by $2: 357986$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$. Since the digit in the ones place in $357986$ is $6$, it is divisible by $2$.
View full question & answer→Question 161 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
AnswerFalse.
If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
Example: $91 (51 + 40)$ is exactly divisible by $13$. However, $13$ does not exactly divide $51$ and $40$.
View full question & answer→Question 171 Mark
Write $'T'$ for true and $'F'$ for false statement.
Every even number is composite.
AnswerFalse.
$2$ is an even number, but it is not composite.
View full question & answer→Question 181 Mark
Find numbers between $1$ and $100$ having exactly three factors.
View full question & answer→Question 191 Mark
Which of the following statements are true? If two numbers are co-primes, at least one of them must be a prime number.
AnswerFalse.
$4$ and $9$ are co-primes but neither of them is a prime number.
View full question & answer→Question 201 Mark
Which of the following numbers are even and which are the odd? $69$
View full question & answer→Question 211 Mark
Fill in the blanks. The smallest prime number is _________________.
AnswerThe smallest prime number is 2.
View full question & answer→Question 221 Mark
Which of the following numbers are even and which are the odd? $50$
View full question & answer→Question 231 Mark
Write the first five multiple of the following numbers: $70$
Answer$70 = 70, 140, 210, 280, 350$
View full question & answer→Question 241 Mark
Which of the following numbers are even and which are the odd? $253$
View full question & answer→Question 251 Mark
List all even prime numbers.
AnswerThe even prime numbers are $2$.
View full question & answer→Question 261 Mark
Test the divisibility of the following numbers by $9$:
$326999$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$.
$326999$ is not divisible by $9$, because the sum of its digits, $3 + 2 + 6 + 9 + 9 + 9$, is $38$, which is not divisible by $9$.
View full question & answer→Question 271 Mark
Which of the following numbers are even and which are the odd? $58$
View full question & answer→Question 281 Mark
Express the following odd numbers as the sum of three odd prime numbers: $49$
View full question & answer→Question 291 Mark
Test the divisibility of the following numbers by $5: 23590$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5.$
$23590$ is divisible by $5$, because the digit at its ones place is $0$.
View full question & answer→Question 301 Mark
Fill in the blanks. Two perfect numbers are ________________ and _________.
AnswerTwo perfect numbers are 6 and 28.
View full question & answer→Question 311 Mark
Write the first five multiple of the following numbers: $17$
Answer$17 = 17, 34, 51, 68, 85$
View full question & answer→Question 321 Mark
Give an example of a number:
Which is divisible by both $2$ and $8$ but not by $16$.
Answer$24$ is divisible by both $2$ and $8$, but not by $16.$
View full question & answer→Question 331 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: A number is divisible by $18$ if it is divisible by both $3$ and $6$.
AnswerFalse.
A number is divisible by $18$ if it is divisible by both $3$ and $6$.
A number has to be divisible by $9$ and $2$ to be divisible by $18$.
Example: $48$ is divisible by $3$ and $6$, but not by $18$.
View full question & answer→Question 341 Mark
Write down all the factors of: $75$
Answer$75 = 1, 3, 5, 15, 25, 75$
View full question & answer→Question 351 Mark
Give an example of a number: Which is divisible by both $3$ and $6$ but not by $18.$
Answer$30$ is divisible by both $3$ and $6$, but not by $18.$
View full question & answer→Question 361 Mark
Test the divisibility of the following numbers by $5$:
$35208$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5$.
$35208$ is not divisible by $5$, because the digit at its ones place is $8$.
View full question & answer→Question 371 Mark
Express the following odd numbers as the sum of three odd prime numbers: $35$
View full question & answer→Question 381 Mark
Test the divisibility of the following numbers by $5: 438750$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5. 438750$ is divisible by $5$, because the digit at its ones place is $0$.
View full question & answer→Question 391 Mark
Write the first five multiple of the following numbers: $65$
Answer$65 = 65, 130, 195, 260, 325$
View full question & answer→Question 401 Mark
Write the smallest odd prime number.
AnswerThe smallest odd prime number is $3$.
View full question & answer→Question 411 Mark
Write $'T'$ for true and $'F'$ for false statement.The sum of two even numbers is always even.
AnswerTrue.
The sum of two even numbers is always even. For example, $4$ and $10$ are even numbers, and their sum, i.e. $14$, is an even number.
View full question & answer→Question 421 Mark
Which of the following statements are true?
$1$ is smallest prime number.
AnswerFalse.
$2$ is the smallest prime number.
View full question & answer→Question 431 Mark
Write $'T'$ for true and $'F'$ for false statement.The sum of two odd numbers is always odd.
AnswerFalse.
The sum of two odd numbers is always even.
For example, $9$ and $11$ are odd numbers, but their sum, i.e. $20,$ is an even number.
View full question & answer→Question 441 Mark
Express the following odd numbers as the sum of three odd prime numbers: $31$
View full question & answer→Question 451 Mark
Test the divisibility of the following numbers by $9$:
$647514$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$.
$647514$ is divisible by $9$, because the sum of its digits, $6 + 4 + 7 + 5 + 1 + 4,$ is $27,$ which is divisible by $9$.
View full question & answer→Question 461 Mark
Express the following numbers as the sum of twin primes: $120$
View full question & answer→Question 471 Mark
Write $'T'$ for true and $'F'$ for false statement. Every prime numbner is odd.
AnswerFalse.
$2$ is an even prime number.
View full question & answer→Question 481 Mark
Which of the following statements are true?
If a number is prime, it must be odd.
AnswerFalse.
$2$ is an even prime number.
View full question & answer→Question 491 Mark
Fill in the blanks.
The smallest composite number is __________.
Answer The smallest composite number is 4.
View full question & answer→Question 501 Mark
Make a list of seven consecutive numbers, none of which is prime.
AnswerThe consecutive numbers are $90, 91, 92, 93, 94, 95, 96.$
View full question & answer→Question 511 Mark
Test the divisibility of the following numbers by $2: 2650$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$. Since the digit in the ones place in $26250$ is $0$, it is divisible by $2.$
View full question & answer→Question 521 Mark
Test the divisibility of the following numbers by $9: 257106$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$.
$257106$ is not divisible by $9$, because the sum of its digits, $2 + 5 + 10 + 6$, is $21$, which is not divisible by $9$.
View full question & answer→Question 531 Mark
Find all the numbers having exactly one factor.
Question 541 Mark
Test the divisibility of the following numbers by $10:$
$63215$
AnswerA number is divisible by $10$ if its ones digit is $0$.
$63215$ is not divisible by $10$, because its ones digit is $5$, not $0$.
View full question & answer→Question 551 Mark
Is there any counting number having no factor at all?
Question 561 Mark
Write the first five multiple of the following numbers: $23$
Answer$23 = 23, 46, 69, 92, 115$
View full question & answer→Question 571 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: The sum of two consecutive odd numbers is always divisible by $4$.
AnswerTrue.
The sum of consecutive odd numbers is always divisible by $4$.
Example: $11$ and $13$ are consecutive odd numbers. $11 + 13 = 24$, which is divisible by $4$.
View full question & answer→Question 581 Mark
Express the following numbers as the sum of twin primes: $144$
View full question & answer→Question 591 Mark
Test the divisibility of the following numbers by $2: 789403$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$.
Since the digit in the ones place in $789403$ is not $0, 2, 4, 6,$ or $8$, it is not divisible by $2.$
View full question & answer→Question 601 Mark
Test the divisibility of the following numbers by $2: 69435$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$.
Since the digit in the ones place in $69435$ is not $0, 2, 4, 6$ or $8$, it is not divisible by $2$.
View full question & answer→Question 611 Mark
Express the following umbers as the sum of two odd primes: $98$
View full question & answer→Question 621 Mark
Test the divisibility of the following numbers by $9: 98712$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$.
$98712$ is divisible by $9$, because the sum of its digits, $9 + 8 + 7 + 1 + 2,$ is $27$, which is divisible by $9.$
View full question & answer→Question 631 Mark
Test the divisibility of the following numbers by $3$:
$524781$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$524781$ is divisible by $3$ because the sum of its digits, $5 + 2 + 4 + 7 + 8 + 1,$ is $27$, which is divisible by $3$.
View full question & answer→Question 641 Mark
Test the divisibility of the following numbers by $4: 35056$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4$.
$35056$ is divisible by $4$ because the number formed by its tens and ones digits is $56$, which is divisible by $4$.
View full question & answer→Question 651 Mark
Which of the following numbers are even and which are the odd?
$32$
View full question & answer→Question 661 Mark
Test the divisibility of the following numbers by $2: 367314$
AnswerA number is divisible by $2$ if its ones digit is $0, 2, 4, 6$ or $8$. Since the digit in the ones place in $367314$ is $4$, it is divisible by $2$.
View full question & answer→Question 671 Mark
Which of the following numbers are even and which are the odd? $37$
View full question & answer→Question 681 Mark
Test the divisibility of the following numbers by $3$:
$20701$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$20701$ is not divisible by $3$ because the sum of its digits, $2 + 0 + 7 + 0 + 1$, is $10$, which is not divisible by $3$.
View full question & answer→Question 691 Mark
Test the divisibility of the following numbers by $4: 946126$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4. 946126$ is not divisible by $4$ because the number formed by its tens and ones digits is $26$, which is not divisible by $4$.
View full question & answer→Question 701 Mark
Test the divisibility of the following numbers by $3$:
$733$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$733$ is not divisible by $3$ because the sum of its digits, $7 + 3 + 3$, is $13,$ which is not divisible by $3.$
View full question & answer→Question 711 Mark
Express the following umbers as the sum of two odd primes: $84$
View full question & answer→Question 721 Mark
Give an example of a number: Which is divisible by $2$ but not by $4$.
Answer$14$ is divisible by $2$, but not by $4$.
View full question & answer→Question 731 Mark
Which of the following numbers are even and which are the odd?
$144$
View full question & answer→Question 741 Mark
Test the divisibility of the following numbers by $4: 2314$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4$.
$2314$ is not divisible by $4$ because the number formed by its tens and ones digits is $14$, which is not divisible by $4$.
View full question & answer→Question 751 Mark
Test the divisibility of the following numbers by $5: 723405$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5. 723405$ is divisible by $5$, because the digit at its ones place is $5$.
View full question & answer→Question 761 Mark
Test the divisibility of the following numbers by $4: 63712$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4$. $63712$ is divisible by $4$ because the number formed by its tens and ones digits is $12$, which is divisible by $4$.
View full question & answer→Question 771 Mark
Test the divisibility of the following numbers by $4: 618$
AnswerA number is divisible by $4$ if the number formed by the digits in its tens and units place is divisible by $4$.
$618$ is not divisible by $4$ because the number formed by its tens and ones digits is $18$, which is not divisible by $4$.
View full question & answer→Question 781 Mark
Express the following numbers as the sum of twin primes: $36$
View full question & answer→Question 791 Mark
Express the following umbers as the sum of two odd primes: $42$
View full question & answer→Question 801 Mark
Express the following umbers as the sum of two odd primes: $36$
View full question & answer→Question 811 Mark
Test the divisibility of the following numbers by $3: 10038$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$10038$ is divisible by $3$ because the sum of its digits, $1 + 0 + 0 + 3 + 8,$ is $12$, which is divisible by $3$.
View full question & answer→Question 821 Mark
Write all the prime numbers between: $10$ and $40$
Answer$10$ and $40 = 11, 13, 17, 19, 23, 29, 31, 37$
View full question & answer→Question 831 Mark
Write all the prime numbers between: $30$ and $40$
Answer$30$ and $40 = 31, 37$
View full question & answer→Question 841 Mark
Fill in the blanks. The $HCF$ of two consecutive odd numbers is ______________.
AnswerThe $HCF$ of two consecutive odd numbers is 1.
View full question & answer→Question 851 Mark
Express the following numbers as the sum of twin primes: $84$
View full question & answer→Question 861 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: If a number is divisible by $4$, it must be divisible by $8$.
AnswerFalse.
If a number is divisible by $4$, it must be divisible by $8$.
Example: $28$ is divisible by $4$ but not divisible by $8$.
View full question & answer→Question 871 Mark
Give an example of a number: Which is divisible by $4$ but not by $8$.
Answer$12$ is divisible by $4$, but not by $8$.
View full question & answer→Question 881 Mark
Fill in the blanks. $1$ is neither ___________ nor _________________.
Answer$1$ is neither prime nor composite.
View full question & answer→Question 891 Mark
Write $(T)$ for true and $(F)$ for false against the following statements: If a number is divisible by $8$, it must be divisible by $4$.
AnswerTrue.
If a number is divisible by $8$, it must be divisible by $4$.
Example: $32$ is divisible by both $8$ and $4$.
View full question & answer→Question 901 Mark
Write down all the factors of: $36$
Answer$36 = 1, 2, 3, 4, 6, 9, 12, 18, 36$
View full question & answer→Question 911 Mark
Write the smallest prime number.
AnswerThe smallest prime number is $2$.
View full question & answer→Question 921 Mark
Test the divisibility of the following numbers by $5: 124684$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5$.
$124684$ is not divisible by $5$, because the digit at its ones place is $4$.
View full question & answer→Question 931 Mark
Test the divisibility of the following numbers by $5: 4965$
AnswerA number is divisible by $5$ if its ones digit is either $0$ or $5$.
$4965$ is divisible by $5$, because the digit at its ones place is $5$.
View full question & answer→Question 941 Mark
Test the divisibility of the following numbers by $9: 2358$
AnswerA number is divisible by $9$ if the sum of its digits is divisible by $9$. $2358$ is divisible by $9$, because the sum of its digits, $2 + 3 + 5 + 8,$ is $18$, which is divisible by $9$.
View full question & answer→Question 951 Mark
Test the divisibility of the following numbers by $3$:
$79124$
AnswerA number is divisible by $3$ if the sum of its digits is divisible by $3$.
$79124$ is not divisible by $3$ because the sum of its digits, $7 + 9 + 1 + 2 + 4,$ is $23$, which is not divisible by $3$.
View full question & answer→Question 961 Mark
Express the following odd numbers as the sum of three odd prime numbers: $63$
View full question & answer→Question 971 Mark
Which of the following numbers are even and which are the odd?
$321$
View full question & answer→Question 981 Mark
Write $(T)$ for true and $(F)$ for false against the following statements:If a number is divisible by both $9$ and $10$, it must be divisible by $90$.
AnswerTrue.
If a number is divisible by both $9$ and $10$, it must be divisible by $90.$
Example: $900$ is both divisible by $9$ and $10$. It is also divisible by $90$.
View full question & answer→