Mixed Divisibility Practice

1) Which number is divisible by 6?

25

45

54

65

54 is divisible by 6 because it’s even and 5 + 4 = 9, which is divisible by 3.

Explanation

54 is divisible by 6 because it’s even and 5 + 4 = 9, which is divisible by 3.

2) Which number is divisible by 8?

45

56

74

75

56 is divisible by 8 because 8 × 7 = 56.

Explanation

56 is divisible by 8 because 8 × 7 = 56.

3) Which number is divisible by 9?

24

36

52

74

36 is divisible by 9 because 3 + 6 = 9.

Explanation

36 is divisible by 9 because 3 + 6 = 9.

4) Which number is divisible by 7?

34

49

65

91

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

Explanation

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

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

15

20

25

30

30 is divisible by both 2 and 3 since it’s even and 3 + 0 = 3.

Explanation

30 is divisible by both 2 and 3 since it’s even and 3 + 0 = 3.

6) 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.

7) Which number is divisible by 4 but not 8?

20

24

32

40

20 is divisible by 4 (20 ÷ 4 = 5) but not by 8.

Explanation

20 is divisible by 4 (20 ÷ 4 = 5) but not by 8.

8) Which number is divisible by 2 but not 4?

14

16

21

24

14 is divisible by 2 (even) but not by 4.

Explanation

14 is divisible by 2 (even) but not by 4.

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

18

27

36

21

21 is divisible by 3 (2 + 1 = 3) but not by 9.

Explanation

21 is divisible by 3 (2 + 1 = 3) but not by 9.

10) Which number is divisible by both 4 and 6?

18

24

35

49

24 is divisible by both 4 and 6 because 24 ÷ 4 = 6 and 24 ÷ 6 = 4.

Explanation

24 is divisible by both 4 and 6 because 24 ÷ 4 = 6 and 24 ÷ 6 = 4.

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

15

21

25

40

40 is divisible by 2, 5, and 10 because it ends in 0 and is even.

Explanation

40 is divisible by 2, 5, and 10 because it ends in 0 and is even.

12) Which number is divisible by 3, 5, and 15?

10

20

30

62

30 is divisible by 3, 5, and 15 because it’s a multiple of each.

Explanation

30 is divisible by 3, 5, and 15 because it’s a multiple of each.

13) Which number is divisible by 7 and 8?

42

56

72

120

56 is divisible by both 7 and 8 because 7 × 8 = 56.

Explanation

56 is divisible by both 7 and 8 because 7 × 8 = 56.

14) Which number is divisible by 2, 4, and 8?

12

20

22

32

32 is divisible by 2, 4, and 8 because 8 × 4 = 32.

Explanation

32 is divisible by 2, 4, and 8 because 8 × 4 = 32.

15) Which number is divisible by 9 and 10?

50

90

100

170

90 is divisible by both 9 (9 + 0 = 9) and 10 (ends in 0).

Explanation

90 is divisible by both 9 (9 + 0 = 9) and 10 (ends in 0).

16) Which number is divisible by 6 and 12?

34

62

72

90

72 is divisible by both 6 and 12 since it’s their common multiple.

Explanation

72 is divisible by both 6 and 12 since it’s their common multiple.

17) Which number is divisible by both 3 and 7?

14

18

21

44

21 is divisible by both 3 and 7 (3 × 7 = 21).

Explanation

21 is divisible by both 3 and 7 (3 × 7 = 21).

18) Which number is divisible by both 5 and 9?

25

45

80

100

45 is divisible by both 5 (ends in 5) and 9 (4 + 5 = 9).

Explanation

45 is divisible by both 5 (ends in 5) and 9 (4 + 5 = 9).

19) Which number is divisible by all numbers from 2 to 5?

20

25

30

60

60 is divisible by all numbers from 2 to 5 because 2 × 3 × 5 = 30, and 60 includes all these factors.

Explanation

60 is divisible by all numbers from 2 to 5 because 2 × 3 × 5 = 30, and 60 includes all these factors.

20) Which number is divisible by 2, 3, 5, and 10?

12

15

30

45

30 is divisible by 2, 3, 5, and 10 — it’s even, ends in 0, and 3 + 0 = 3.

Explanation

30 is divisible by 2, 3, 5, and 10 — it’s even, ends in 0, and 3 + 0 = 3.