Divisibility Rules 2�10: Identify Factors & Multiples

1) Which rule checks divisibility by 2?

Last digit even

Digit sum divisible by 3

Last digit 0 or 5

Last two digits divisible by 4

A number is divisible by 2 if its last digit is even.

Explanation

A number is divisible by 2 if its last digit is even.

2) Which number is divisible by both 5 and 10?

25

50

75

95

50 is divisible by both 5 and 10 because it ends in 0.

Explanation

50 is divisible by both 5 and 10 because it ends in 0.

3) Which number is divisible by both 2 and 3?

14

18

20

25

18 is divisible by both 2 and 3 — it’s even and its digits add to 9.

Explanation

18 is divisible by both 2 and 3 — it’s even and its digits add to 9.

4) Which rule checks divisibility by 10?

Ends in 2, 4, 6, 8

Ends in 3, 6, 9

Ends in 0

Ends in 5 or 7

A number is divisible by 10 if it ends in 0.

Explanation

A number is divisible by 10 if it ends in 0.

5) Which rule checks divisibility by 9?

Last digit even

Last two digits divisible by 4

Digit sum divisible by 9

Ends in 0 or 5

A number is divisible by 9 if the sum of its digits is divisible by 9.

Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9.

6) Which rule checks divisibility by 8?

Last digit even

Last three digits divisible by 8

Last digit 0 or 5

Sum of digits divisible by 3

A number is divisible by 8 if its last three digits form a number divisible by 8.

Explanation

A number is divisible by 8 if its last three digits form a number divisible by 8.

7) Which rule checks divisibility by 6?

Number divisible by 2 and 3

Number divisible by 2 and 5

Number divisible by 3 and 9

Number divisible by 4 and 5

A number is divisible by 6 if it’s divisible by both 2 and 3.

Explanation

A number is divisible by 6 if it’s divisible by both 2 and 3.

8) Which rule checks divisibility by 5?

Last digit even

Last digit 0 or 5

Sum of digits divisible by 3

Last two digits divisible by 4

A number is divisible by 5 if its last digit is 0 or 5.

Explanation

A number is divisible by 5 if its last digit is 0 or 5.

9) Which rule checks divisibility by 3?

Last digit even

Last digit 0 or 5

Sum of digits divisible by 3

Last two digits divisible by 4

A number is divisible by 3 if the sum of its digits is divisible by 3.

Explanation

A number is divisible by 3 if the sum of its digits is divisible by 3.

10) Which number is divisible by 2?

15

27

42

99

42 is divisible by 2 because its last digit (2) is even.

Explanation

42 is divisible by 2 because its last digit (2) is even.

11) Which of these is divisible by both 2 and 5?

15

22

45

40

40 is divisible by both 2 and 5 because it ends in 0 (which makes it even and a multiple of 5).

Explanation

40 is divisible by both 2 and 5 because it ends in 0 (which makes it even and a multiple of 5).

12) Which number is divisible by 10?

23

70

77

95

70 is divisible by 10 because it ends in 0.

Explanation

70 is divisible by 10 because it ends in 0.

13) Which number is divisible by 9?

25

355

41

81

81 is divisible by 9 because the sum of its digits (8 + 1 = 9) is a multiple of 9.

Explanation

81 is divisible by 9 because the sum of its digits (8 + 1 = 9) is a multiple of 9.

14) Which number is divisible by 8?

22

32

44

63

32 is divisible by 8 because 8 × 4 = 32.

Explanation

32 is divisible by 8 because 8 × 4 = 32.

15) Which number is divisible by 7?

15

22

49

50

49 is divisible by 7 because 7 × 7 = 49.

Explanation

49 is divisible by 7 because 7 × 7 = 49.

16) Which number is divisible by 6?

25

33

48

55

48 is divisible by 6 because it is even (divisible by 2) and the sum of its digits (4 + 8 = 12) is divisible by 3.

Explanation

48 is divisible by 6 because it is even (divisible by 2) and the sum of its digits (4 + 8 = 12) is divisible by 3.

17) Which number is divisible by 5?

42

66

77

90

90 is divisible by 5 because it ends in 0.

Explanation

90 is divisible by 5 because it ends in 0.

18) Which number is divisible by 4?

11

28

45

63

28 is divisible by 4 because the last two digits, 28, are divisible by 4.

Explanation

28 is divisible by 4 because the last two digits, 28, are divisible by 4.

19) Which number is divisible by 3?

14

27

32

41

27 is divisible by 3 because the sum of its digits (2 + 7 = 9) is a multiple of 3.

Explanation

27 is divisible by 3 because the sum of its digits (2 + 7 = 9) is a multiple of 3.

20) Which rule checks divisibility by 4?

Last two digits divisible by 4

Ends in 0 or 5

Alternating digit sum divisible by 11

Last digit even

A number is divisible by 4 if its last two digits form a number divisible by 4.

Explanation

A number is divisible by 4 if its last two digits form a number divisible by 4.

Divisibility Basics

1) Which rule checks divisibility by 2?

2) Which number is divisible by both 5 and 10?

3) Which number is divisible by both 2 and 3?

4) Which rule checks divisibility by 10?

5) Which rule checks divisibility by 9?

6) Which rule checks divisibility by 8?

7) Which rule checks divisibility by 6?

8) Which rule checks divisibility by 5?

9) Which rule checks divisibility by 3?

10) Which number is divisible by 2?

11) Which of these is divisible by both 2 and 5?

12) Which number is divisible by 10?

13) Which number is divisible by 9?

14) Which number is divisible by 8?

15) Which number is divisible by 7?

16) Which number is divisible by 6?

17) Which number is divisible by 5?

18) Which number is divisible by 4?

19) Which number is divisible by 3?

20) Which rule checks divisibility by 4?