Applying Divisibility Proofs in Problems

1) If a number leaves remainder 1 when divided by 3, which equation represents it?

N = 3k

N = 3k + 1

N = 3k + 2

N = 3k − 1

2) Which value of x makes 5x + 2 divisible by 3?

X = 1

X = 2

X = 4

X = 6

3) A number is divisible by 4 and leaves remainder 1 when divided by 3. Which equation represents it?

N = 3k + 1

N = 4k

N = 4k + 3

N = 12k + 4

4) Which number satisfies both: divisible by 6 and leaves remainder 2 when divided by 5?

10

22

32

42

5) Solve for x: 2x + 3 is divisible by 5. Which x works?

X = 1

X = 2

X = 3

X = 4

6) Which number leaves remainder 4 when divided by both 5 and 7?

24

39

49

74

7) If x is an even number and 3x + 1 is divisible by 5, which of these could x be?

4

6

8

10

8) Which of the following equations represents numbers that are divisible by both 2 and 3 but leave remainder 1 when divided by 5?

N = 5k

N = 6k + 5

N = 5k + 1

N = 30k + 6

9) Which number is divisible by 6 but not by 9?

18

24

36

45

10) A number divided by 8 leaves remainder 3. Which equation models this?

N = 8k

N = 8k + 1

N = 8k + 3

N = 8k + 5

11) Solve for x: 4x − 7 = 3x + 5

X = 7

X = 12

X = 15

X = 20

12) Find the smallest number greater than 50 that is divisible by both 4 and 6.

52

54

56

60

13) Which number is divisible by 5 and leaves remainder 2 when divided by 3?

10

15

20

25

14) Which value of x makes 7x + 2 divisible by 3?

X = 1

X = 2

X = 3

X = 5

15) A number is divisible by both 5 and 9. Which equation represents it?

N = 5k + 9

N = 9k + 5

N = 10k

N = 45k