Maths 1 Mark Question

True.
Solution:
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.

20 = 1, 2, 4, 5, 10, 20

True.
Solution:
For example, 4 and 6 are two numbers whose HCF is 2 and LCM is 12, but 2 is a factor of 12.

A 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.

A 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.

A 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.

80 and 100 = 83, 89, 97

True.
Solution:
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.

40 and 80 = 41, 43, 47, 53, 59, 61, 67, 71, 73, 79

60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

A number is divisible by 10 if its ones digit is 0.
5790 is divisible by 10, because its ones digit is 0.

A 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.

A 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.

False.
Solution:
3 and 7 are two prime numbers and their sum is 10, which is even.

A 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.

False.
Solution:
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.

False.
Solution:
2 is an even number, but it is not composite.

4, 9, 25, 49.

False.
Solution:
4 and 9 are co-primes but neither of them is a prime number.

59 = Odd.

The smallest prime number is 2.

50 = Even.

70 = 70, 140, 210, 280, 350

253 = Odd.

The even prime numbers are 2.

A 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.

58 = Even.

49 = 3 + 5 + 41

A 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.

Two perfect numbers are 6 and 28.

17 = 17, 34, 51, 68, 85

24 is divisible by both 2 and 8, but not by 16.

False.
Solution:
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.

75 = 1, 3, 5, 15, 25, 75

30 is divisible by both 3 and 6, but not by 18.

A 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.

35 = 5 + 7 + 23

A 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.

65 = 65, 130, 195, 260, 325

The smallest odd prime number is 3.

True.
Solution:
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.

False.
Solution:
2 is the smallest prime number.

False.
Solution:
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.

31 = 5 + 7 + 19

A 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.

120 = 59 + 61

False.
Solution:
2 is an even prime number.

False.
Solution:
2 is an even prime number.

The smallest composite number is 4.

The consecutive numbers are 90, 91, 92, 93, 94, 95, 96.

A 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.

A 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.

1.

A 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.

No.

23 = 23, 46, 69, 92, 115

True.
Solution:
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.

144 = 71 + 73

A 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.

A 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.

98 = 79 + 19

A 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.

A 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.

A 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.

32 = Even.

A 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.

37 = Odd.

A 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.

A 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.

A 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.

84 = 17 + 67

14 is divisible by 2, but not by 4.

144 = Even.

A 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.

A 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.

A 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.

A 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.

36 = 17 + 19

42 = 5 + 37

36 = 7 + 29

A 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.

10 and 40 = 11, 13, 17, 19, 23, 29, 31, 37

30 and 40 = 31, 37

The HCF of two consecutive odd numbers is 1.

84 = 41 + 43

False.
Solution:
If a number is divisible by 4, it must be divisible by 8.
Example: 28 is divisible by 4 but not divisible by 8.

12 is divisible by 4, but not by 8.

1 is neither prime nor composite.

True.
Solution:
If a number is divisible by 8, it must be divisible by 4.
Example: 32 is divisible by both 8 and 4.

36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

The smallest prime number is 2.

A 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.

A 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.

A 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.

A 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.

63 = 7 + 13 + 43

321 = Odd.

True.
Solution:
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.