How do you use divisibility rules to

determine is a number is prime or composite?

A number is divisible by another number if the quotient is a whole number with no remainder.

42 ÷ 6 = 7 Quotient

Divisibility RulesDivisibility RulesA number is divisible by. . . Divisible Not Divisible

2 if the last digit is even (0, 2, 4, 6, or 8). 3,978 4,975

3 if the sum of the digits is divisible by 3. 315 139

4 if the last two digits form a number divisible by 4.

8,512 7,518

5 if the last digit is 0 or 5. 14,975 10,978

6 if the number is divisible by both 2 and 3 48 20

9 if the sum of the digits is divisible by 9. 711 93

10 if the last digit is 0. 15,990 10,536

2

3

4

5Not

divisible

So 462 is divisible by 2 and 3.

The last digit, 2, is even.

The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3.

The last two digits form the number 62. 62 is not divisible by 4.

Divisible

Divisible

Not divisible

The last digit is 2.

Example 1: Checking Divisibility

Tell whether 462 is divisible by 2, 3, 4, and 5.

Example 1B: Checking Divisibility

Tell whether 540 is divisible by 6, 9, and 10.

6

9

10

So 540 is divisible by 6, 9, and 10.

The number is divisible by both 2 and 3.

The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9.

The last digit is 0.

Divisible

Divisible

Divisible

Check It Out: Example 1A

Tell whether 114 is divisible by 2, 3, 4, and 5.

2

3

4

5Not

Divisible

So 114 is divisible by 2 and 3.

The last digit, 4, is even.

The sum of the digits is 1 + 1 + 4 = 6. 6 is divisible by 3.

The last two digits form the number 14. 14 is not divisible by 4.

Divisible

Divisible

Not Divisible

The last digit is 4.

Check It Out: Example 1B

Tell whether 810 is divisible by 6, 9, and 10.

6

9

10

So 810 is divisible by 6, 9, and 10.

The number is divisible by both 2 and 3.

The sum of the digits is 8 + 1 + 0 = 9. 9 is divisible by 9.

The last digit is 0.

Divisible

Divisible

Divisible

Any number greater than 1 is divisible by at least two numbers—1 and the number itself. Numbers that are divisible by more than two numbers are called composite numbers.

A prime number is divisible by only the numbers 1 and itself. For example, 11 is a prime number because it is divisible by only 1 and 11. The numbers 0 and 1 are neither prime nor composite.

Click to see which numbers from 1 through 50 are prime.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

C. 31

divisible by 1, 31

prime

D. 18

divisible by 1, 2, 3, 6, 9, 18

composite

Tell whether each number is prime or composite.

Tell whether each number is prime or composite.

A. 27

divisible by 1, 3, 9, 27

composite

B. 24

divisible by 1, 2, 3, 4, 6, 8, 12, 24

composite

Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, and 10.

1. 256

2. 720

3. 615

Tell whether each number is prime or composite.

4. 47 5. 38

divisible by 2, 3, 4, 5, 6, 9, 10

divisible by 2, 4

divisible by 3, 5

prime composite