Applying Divisibility Rules In Patterns

1) Which number is divisible by 2 but not 5?

14

20

25

30

Even, but doesn’t end in 0 or 5.

Explanation

Even, but doesn’t end in 0 or 5.

2) Which number is divisible by 5 and ends in 5?

20

30

36

35

Ends in 5 → divisible by 5.

Explanation

Ends in 5 → divisible by 5.

3) Which number in {32, 36, 38, 40} is divisible by 3?

32

36

38

40

3+6=9 → divisible by 3.

Explanation

3+6=9 → divisible by 3.

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

8

12

None – if a number is divisible by 4, it is always divisible by 2

24

If a number is divisible by 4, it’s always divisible by 2.

Explanation

If a number is divisible by 4, it’s always divisible by 2.

5) Which of these is divisible by 9?

70

81

83

85

8+1=9 → divisible by 9.

Explanation

8+1=9 → divisible by 9.

6) Which number is divisible by 2, 3, and 6?

60

65

70

75

Even, digit sum 6, so divisible by all.

Explanation

Even, digit sum 6, so divisible by all.

7) Which of these is divisible by 3?

19

20

21

22

2+1=3 → divisible by 3.

Explanation

2+1=3 → divisible by 3.

8) Which of these numbers is divisible by 6?

20

25

30

35

Divisible by both 2 (even) and 3 (3+0=3).

Explanation

Divisible by both 2 (even) and 3 (3+0=3).

9) Which of these is divisible by 4?

18

28

35

45

Last two digits = 28 ÷ 4 = 7.

Explanation

Last two digits = 28 ÷ 4 = 7.

10) Which number is divisible by 5 and 10?

15

25

55

50

Ends in 0.

Explanation

Ends in 0.

11) Which number in the set {12, 18, 25, 30} is not divisible by 3?

12

18

25

30

2+5=7, not divisible by 3.

Explanation

2+5=7, not divisible by 3.

12) Which number is divisible by both 3 and 9?

12

27

21

30

2+7=9 → divisible by 9 (so also by 3).

Explanation

2+7=9 → divisible by 9 (so also by 3).

13) Which number is divisible by 5?

13

25

37

49

Ends in 5.

Explanation

Ends in 5.

14) Which number in {40, 42, 44, 46} is divisible by 3?

42

40

44

46

4+2=6 → divisible by 3.

Explanation

4+2=6 → divisible by 3.

15) Which number is divisible by 2 and 3?

10

16

12

14

Even and digit sum 3 → divisible by 6 too.

Explanation

Even and digit sum 3 → divisible by 6 too.

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

14

20

24

32

20 ÷ 4 = 5, but not divisible by 8.

Explanation

20 ÷ 4 = 5, but not divisible by 8.

17) Which number is divisible by 6?

36

45

52

70

36 is divisible by 2 (even) and by 3 (digit sum 9).

Explanation

36 is divisible by 2 (even) and by 3 (digit sum 9).

18) Which of these is divisible by 9?

62

81

85

91

8+1=9 → divisible by 9.

Explanation

8+1=9 → divisible by 9.

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

15

22

20

25

Ends in 0.

Explanation

Ends in 0.

20) Which of these numbers is divisible by 10?

24

35

50

72

Ends in 0.

Explanation

Ends in 0.

Applying Divisibility Rules in Patterns

1) Which number is divisible by 2 but not 5?

2) Which number is divisible by 5 and ends in 5?

3) Which number in {32, 36, 38, 40} is divisible by 3?

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

5) Which of these is divisible by 9?

6) Which number is divisible by 2, 3, and 6?

7) Which of these is divisible by 3?

8) Which of these numbers is divisible by 6?

9) Which of these is divisible by 4?

10) Which number is divisible by 5 and 10?

11) Which number in the set {12, 18, 25, 30} is not divisible by 3?

12) Which number is divisible by both 3 and 9?

13) Which number is divisible by 5?

14) Which number in {40, 42, 44, 46} is divisible by 3?

15) Which number is divisible by 2 and 3?

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

17) Which number is divisible by 6?

18) Which of these is divisible by 9?

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

20) Which of these numbers is divisible by 10?