Maths 2 Mark Question

A number is divisible by 6 if it is divisible by both 2 and 3.
Since 251780 is not divisible by 3, it is not divisible by 6.
Checking the divisibility by 3: The sum of the digits of the number, 2 + 5 + 1 + 7 + 8 + 0, is 23, which is not divisible by 3.
So, the number is not divisible by 3.

12030624 by 8
12030624 is divisible by 8.
It is because the number formed by its hundreds, tens and ones digits is 624, which is divisible by 8.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
137 is a prime number, because it is not divisible by 2, 3, 5, 7 and 11.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
2345 is divisible by 7.
We have 234 - 2 × 5 = 224, which is a multiple of 7.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
331 is a prime number, because it is not divisible by 2, 3, 5, 7, 11, 13, 17 and 19.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
6021 is divisible by 7.
We have 602 - 2 × 1 = 600, which is not a multiple of 7.

53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are the prime numbers between 50 and 100.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
161 is a not prime number, because it is divisible by 7.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
397 is a prime number, because it is not divisible by 2, 3, 5, 7, 11, 13, 17 and 19.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
14126 is divisible by 7.
We have 1412 - 2 × 6 = 1400, which is a multiple of 7.

10001001 by 3
10001001 is divisible by 3.
It is because the sum of its digits, 1 + 0 + 0 + 0 + 1 + 0 + 0 + 1, is 3, which is divisible by 3.

COMPOSITE NUMBERS: Numbers having more than two factors are known as composite numbers.
Yes a composite number can odd. The smallest odd composite number is 9.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
66311 is not divisible by 11.
Sum of the digits at odd places = (1 + 3 + 6) = 10
Sum of the digits at even places = (1 + 6) = 7
Difference of the two sums = (10 - 7) = 3, which is not divisible by 11.

Seven consecutive composite numbers less than 100 having no prime number between them are 90, 91, 92, 93, 94, 95 and 96.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
137269 is divisible by 11.
Sum of the digits at odd places = (9 + 2 + 3) = 14
Sum of the digits at even places = (6 + 7 + 1) = 14
Difference of the two sums = (14 - 14) = 0, which is a divisible by 11.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
If their difference is a multiple of 7, the number is divisible by 7.
826 is divisible by 7.
We have 82 - 2 × 6 = 70, which is a multiple of 7.

10000001 by 11
10000001 is divisible by 11.
Sum of digits at odd places = (1 + 0 + 0 + 0) = 1
Sum of digits at even places = (0 + 0 + 0 + 1) = 1
Difference of the two sums = (1 - 1) = 0, which is divisible by 11.

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
901674 is not divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 674, is not divisible by 8.

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
36792 is divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 792, is divisible by 8

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
1790184 is divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 184, is divisible by 8.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
217 is a not prime number, because it is divisible by 7.

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
2138 is not divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 138, is not divisible by 8.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
4334 is divisible by 11.
Sum of the digits at odd places = (4 + 3) = 7
Sum of the digits at even places = (3 + 4) = 7
Difference of the two sums = (7 - 7) = 0, which is divisible by 11.

A number is divisible by 6 if it is divisible by both 2 and 3.Since 872536 is not divisible by 3, it is not divisible by 6.
Checking the divisibility by 3: The sum of the digits of the number, 8 + 7 + 2 + 5 + 3 + 6, is 31, which is not divisible by 3.
So, the number is not divisible by 3.

2134563 by 9
2134563 is not divisible by 9.
It is because the sum of its digits, 2 + 1 + 3 + 4 + 5 + 6 + 3, is 24, which is not divisible by 9.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
103 is a prime number, because it is not divisible by 2, 3, 5, 7, 11 and 13.

10203574 by 4
10203574 is not divisible by 4.
It is because the number formed by its tens and the ones digits is 74, which is not divisible by 4.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
117 is not divisible by 7.
We have 11 - 2 × 7 = -3, which is not a multiple of 7.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
83721 is divisible by 11.
Sum of the digits at odd places = (1 + 7 + 8) = 16
Sum of the digits at even places = (2 + 3) = 5
Difference of the two sums = (16 - 5) = 11, which is divisible by 11.

To determine if a number is divisible by 7, double the last digit of the number and subtract it from the number formed by the remaining digits.
25368 is divisible by 7.
We have 2536 - 2 × 8 = 2520, which is a multiple of 7.

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
9364 is not divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 364, is not divisible by 8.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
901351 is divisible by 11.
Sum of the digits at odd places = (0 + 3 + 1) = 4
Sum of the digits at even places = (9 + 1 + 5) = 15
Difference of the two sums = (4 - 15) = -11, which is divisible by 11.

A number is divisible by 6 if it is divisible by both 2 and 3.
Since 71232 is divisible by both 2 and 3, it is divisible by 6.
Checking the divisibility by 2: Since the number has 2 in its units place, it is divisible by 2.
Checking the divisibility by 3: The sum of the digits of the number, 7 + 1 + 2 + 3 + 2, is 15, which is divisible by 3.
So, the number is divisible by 3.

A number is divisible by 6 if it is divisible by both 2 and 3.
Since 934706 is not divisible by 3, it is not divisible by 6.
Checking the divisibility by 3: Since the sum of the digits of the number, 9 + 3 + 4 + 7 + 0 + 6, is 29, which is not divisible by 3.
So, the number is not divisible by 3.

67529124A number is divisible by 8 if the number formed by the hundreds, tens and ones digits is divisible by 8.
Since the digits at the hundred’s, ten’s and unit places are 124, which is not divisible by 8, 67529124 is not divisible by 8.

A number is divisible by 8 if the number formed by the last three digits (digits in the hundreds, tens and units places) is divisible by 8.
136976 is divisible by 8.
It is because the number formed by its hundreds, tens and ones digits, i.e., 976, is divisible by 8.

A number is divisible by 6 if it is divisible by both 2 and 3.
Since 2070 is divisible by 2 and 3, it is divisible by 6.
Checking the divisibility by 2: Since the number 2070 has 0 in its units place, it is divisible by 2.
Checking the divisibility by 3: The sum of the digits of 2070, 2 + 0 + 7 + 0, is 9, which is divisible by 3.
So, it is divisible by 3.

A number is divisible by 6 if it is divisible by both 2 and 3.
Since 46523 is not divisible by 2, it is not divisible by 6.
Checking the divisibility by 2: Since the number 46523 has 3 in its units place, it is not divisible by 2.

No, they cannot have 512 as their LCM.
We know that the HCF is one of the factors of the LCM.
Here, 3, which is a factor of 12, is not a factor of 512.

A number is divisible by 11 if the difference of the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.
8790322 is not divisible by 11.
Sum of the digits at odd places = (2 + 3 + 9 + 8) = 22.
Sum of the digits at even places = (2 + 0 + 7) = 9
Difference of the two sums = (22 - 9) = 13, which is not divisible by 11.

19083625 by 11
19083625 is divisible by 11.
Sum of digits at odd places = (5 + 6 + 8 + 9) = 28
Sum of digits at even places = (2 + 3 + 0 + 1) = 6
Difference of the two sums = (28 - 6) = 22, which is divisible by 11.

CO-PRIMES: Two numbers are said to be co-primes if they do not have a common factor other than 1.
No, co-primes are not be always primes.
For example 6, 7 are co-primes, while 6 is not a prime number.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
277 is a prime number, because it is not divisible by 2, 3, 5, 7, 11, 13, 17 and 19.

TWIN PRIMES: Two consecutive odd prime numbers are known as twin primes.
(59, 61), (71, 73) are the pairs of twin primes between 50 and 100.

A number between 100 and 200 is a prime number if it is not divisible by any prime number less than 15.
Similarly, a number between 200 and 300 is a prime number if it is not divisible by any prime number less than 20.
179 is a prime number, because it is not divisible by 2, 3, 5, 7, 11 and 13.

Each of the numbers which have exactly two factors, namely, 1 and itself, is called a Prime Number.
Example- The numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. are all prime number.