Using Divisibility Rules

1) A number ending in 0 is always divisible by:

3

10

7

9

A number that ends in 0 is divisible by 10 because it can be expressed as 10 multiplied by an integer. This is based on the definition of divisibility, where a number is divisible by another if the division results in an integer without a remainder.

Explanation

A number that ends in 0 is divisible by 10 because it can be expressed as 10 multiplied by an integer. This is based on the definition of divisibility, where a number is divisible by another if the division results in an integer without a remainder.

2) A number is divisible by 3 if:

It ends in 5

It is even

The sum of its digits is divisible by 3

It ends in 0

A number is divisible by 3 if the sum of its digits is divisible by 3. This rule helps easily determine divisibility without performing more complex calculations. For example, the number 123 has a digit sum of 1 + 2 + 3 = 6, which is divisible by 3, hence 123 is divisible by 3.

Explanation

A number is divisible by 3 if the sum of its digits is divisible by 3. This rule helps easily determine divisibility without performing more complex calculations. For example, the number 123 has a digit sum of 1 + 2 + 3 = 6, which is divisible by 3, hence 123 is divisible by 3.

3) Which number is divisible by 5?

42

63

75

88

A number is divisible by 5 if it ends in 0 or 5. In this case, 75 ends with a 5, making it divisible by 5, while the other options do not.

Explanation

A number is divisible by 5 if it ends in 0 or 5. In this case, 75 ends with a 5, making it divisible by 5, while the other options do not.

4) Which of these is divisible by 10?

23

55

90

97

A number is divisible by 10 if it ends with a 0. Among the options, only 90 ends with a 0, making it the only number divisible by 10.

Explanation

A number is divisible by 10 if it ends with a 0. Among the options, only 90 ends with a 0, making it the only number divisible by 10.

5) Which number is divisible by 9?

25

53

81

92

A number is divisible by 9 if the sum of its digits is also divisible by 9. For the number 81, the sum of the digits (8 + 1 = 9) is divisible by 9, which confirms that 81 is divisible by 9. The other options, 25 (2 + 5 = 7), 53 (5 + 3 = 8), and 92 (9 + 2 = 11), do not meet this criterion.

Explanation

A number is divisible by 9 if the sum of its digits is also divisible by 9. For the number 81, the sum of the digits (8 + 1 = 9) is divisible by 9, which confirms that 81 is divisible by 9. The other options, 25 (2 + 5 = 7), 53 (5 + 3 = 8), and 92 (9 + 2 = 11), do not meet this criterion.

6) Which number is divisible by 6?

11

15

24

35

A number is divisible by 6 if it is divisible by both 2 and 3. The number 24 is even, thus divisible by 2, and the sum of its digits (2 + 4) equals 6, which is divisible by 3. Therefore, 24 is divisible by 6, while the other options are not.

Explanation

A number is divisible by 6 if it is divisible by both 2 and 3. The number 24 is even, thus divisible by 2, and the sum of its digits (2 + 4) equals 6, which is divisible by 3. Therefore, 24 is divisible by 6, while the other options are not.

7) Which is divisible by 4?

14

28

29

45

A number is divisible by 4 if the number divided by 4 results in a whole number without a remainder. In this case, 28 divided by 4 equals 7, which is a whole number, confirming that 28 is divisible by 4. The other numbers do not satisfy this condition.

Explanation

A number is divisible by 4 if the number divided by 4 results in a whole number without a remainder. In this case, 28 divided by 4 equals 7, which is a whole number, confirming that 28 is divisible by 4. The other numbers do not satisfy this condition.

8) Which number is divisible by both 2 and 5?

12

15

18

20

A number is divisible by both 2 and 5 if it ends in 0. Among the given options, only 20 ends with a 0, making it divisible by both 2 and 5.

Explanation

A number is divisible by both 2 and 5 if it ends in 0. Among the given options, only 20 ends with a 0, making it divisible by both 2 and 5.

9) Which number is divisible by 2 but not by 3?

14

18

24

30

To determine which number is divisible by 2 but not by 3, we check each option. 14 is divisible by 2 (14 ÷ 2 = 7) and not by 3 (14 ÷ 3 = 4.67). 18 is divisible by both 2 and 3, 24 is divisible by both, and 30 is also divisible by both. Thus, the correct answer is 14.

Explanation

To determine which number is divisible by 2 but not by 3, we check each option. 14 is divisible by 2 (14 ÷ 2 = 7) and not by 3 (14 ÷ 3 = 4.67). 18 is divisible by both 2 and 3, 24 is divisible by both, and 30 is also divisible by both. Thus, the correct answer is 14.

10) Which of these numbers is divisible by 3?

14

25

27

41

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 27 (2 + 7 = 9) is divisible by 3, while 14 (1 + 4 = 5), 25 (2 + 5 = 7), and 41 (4 + 1 = 5) are not.

Explanation

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 27 (2 + 7 = 9) is divisible by 3, while 14 (1 + 4 = 5), 25 (2 + 5 = 7), and 41 (4 + 1 = 5) are not.

11) A number is divisible by 4 if:

Its last two digits form a number divisible by 4

It ends in 0

Its digits add to 9

It ends in 5

A number is considered divisible by 4 if the number formed by its last two digits is divisible by 4. This is because of how numbers are structured in the decimal system, where the last two digits determine divisibility by 4.

Explanation

A number is considered divisible by 4 if the number formed by its last two digits is divisible by 4. This is because of how numbers are structured in the decimal system, where the last two digits determine divisibility by 4.

12) Which number is divisible by 5 but not 10?

30

45

50

100

A number is divisible by 5 if it ends in 0 or 5. However, to not be divisible by 10, it must not end in 0. Among the options, 45 ends in 5 and is divisible by 5, while the others (30, 50, 100) are all divisible by 10 since they end in 0.

Explanation

A number is divisible by 5 if it ends in 0 or 5. However, to not be divisible by 10, it must not end in 0. Among the options, 45 ends in 5 and is divisible by 5, while the others (30, 50, 100) are all divisible by 10 since they end in 0.

13) Which of these is divisible by 2, 3, and 6?

18

25

32

45

A number is divisible by 2 if it is even, by 3 if the sum of its digits is divisible by 3, and by 6 if it meets both criteria. The number 18 is even (divisible by 2), the sum of its digits (1 + 8 = 9) is divisible by 3, and thus it is also divisible by 6. The other options do not meet these criteria.

Explanation

A number is divisible by 2 if it is even, by 3 if the sum of its digits is divisible by 3, and by 6 if it meets both criteria. The number 18 is even (divisible by 2), the sum of its digits (1 + 8 = 9) is divisible by 3, and thus it is also divisible by 6. The other options do not meet these criteria.

14) Which number is divisible by 10?

42

70

75

99

A number is divisible by 10 if it ends in 0. Among the options, only 70 ends in 0, making it the only number that is divisible by 10.

Explanation

A number is divisible by 10 if it ends in 0. Among the options, only 70 ends in 0, making it the only number that is divisible by 10.

15) Which of these numbers is divisible by 3?

16

21

22

25

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 21 has a digit sum of 2 + 1 = 3, which is divisible by 3. In contrast, 16 (1 + 6 = 7), 22 (2 + 2 = 4), and 25 (2 + 5 = 7) are not divisible by 3.

Explanation

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 21 has a digit sum of 2 + 1 = 3, which is divisible by 3. In contrast, 16 (1 + 6 = 7), 22 (2 + 2 = 4), and 25 (2 + 5 = 7) are not divisible by 3.

16) Which number is divisible by 2, 5, and 10?

15

25

40

45

A number is divisible by another if it can be divided evenly without leaving a remainder. The number 40 is divisible by 2, 5, and 10 because: 40 ÷ 2 = 20, 40 ÷ 5 = 8, and 40 ÷ 10 = 4, all of which are whole numbers.

Explanation

A number is divisible by another if it can be divided evenly without leaving a remainder. The number 40 is divisible by 2, 5, and 10 because: 40 ÷ 2 = 20, 40 ÷ 5 = 8, and 40 ÷ 10 = 4, all of which are whole numbers.

17) Which number is divisible by 4?

33

50

60

75

A number is divisible by 4 if the last two digits form a number that is divisible by 4. In this case, 60 is divisible by 4 (60 ÷ 4 = 15), while 33, 50, and 75 are not.

Explanation

A number is divisible by 4 if the last two digits form a number that is divisible by 4. In this case, 60 is divisible by 4 (60 ÷ 4 = 15), while 33, 50, and 75 are not.

18) Which is divisible by 6 but not by 3?

18

24

None – all multiples of 6 are also divisible by 3

36

A number is divisible by 6 if it meets the criteria of being even and the sum of its digits is divisible by 3. However, all multiples of 6 (like 6, 12, 18, 24, etc.) are inherently also divisible by 3, as 3 is a factor of 6. Therefore, there cannot be a number that is divisible by 6 but not by 3.

Explanation

A number is divisible by 6 if it meets the criteria of being even and the sum of its digits is divisible by 3. However, all multiples of 6 (like 6, 12, 18, 24, etc.) are inherently also divisible by 3, as 3 is a factor of 6. Therefore, there cannot be a number that is divisible by 6 but not by 3.

19) Which of these numbers is divisible by 9?

72

74

76

78

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 72 has a digit sum of 7 + 2 = 9, which is divisible by 9. The other options (74, 76, and 78) do not have digit sums that are divisible by 9.

Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 72 has a digit sum of 7 + 2 = 9, which is divisible by 9. The other options (74, 76, and 78) do not have digit sums that are divisible by 9.

20) Which of these is not divisible by 9?

28

36

45

54

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, the number 28 has digits that sum to 10 (2 + 8), which is not divisible by 9. In contrast, the sums of the digits for 36 (9), 45 (9), and 54 (9) are all divisible by 9.

Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. For example, the number 28 has digits that sum to 10 (2 + 8), which is not divisible by 9. In contrast, the sums of the digits for 36 (9), 45 (9), and 54 (9) are all divisible by 9.