1. How do you use divisibility rules to determine is a number is prime or composite?

2. A number is divisible by another number if the quotient is a whole number with no remainder.
42 ÷ 6 = 7
Quotient

3. Divisibility Rules A 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

4. Example 1: Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5
The last digit, 2, is even.
Divisible
The sum of the digits is = is divisible by 3.
Divisible
The last two digits form the number is not divisible by 4.
Not divisible
Not divisible
The last digit is 2.
So 462 is divisible by 2 and 3.

5. Example 1B: Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10. 6 9 10
The number is divisible by both 2 and 3.
Divisible
The sum of the digits is = is divisible by 9.
Divisible
The last digit is 0.
Divisible
So 540 is divisible by 6, 9, and 10.

6. So 114 is divisible by 2 and 3. 2 3 4 5 The last digit, 4, is even.
Check It Out: Example 1A
Tell whether 114 is divisible by 2, 3, 4, and 5. 2 3 4 5
The last digit, 4, is even.
Divisible
The sum of the digits is = is divisible by 3.
Divisible
The last two digits form the number is not divisible by 4.
Not Divisible
Not Divisible
The last digit is 4.
So 114 is divisible by 2 and 3.

7. Check It Out: Example 1B
Tell whether 810 is divisible by 6, 9, and 10. 6 9 10
The number is divisible by both 2 and 3.
Divisible
The sum of the digits is = is divisible by 9.
Divisible
The last digit is 0.
Divisible
So 810 is divisible by 6, 9, and 10.

8. 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.

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

10. Tell whether each number is prime or composite.
divisible by 1, 31
prime
D. 18
divisible by 1, 2, 3, 6, 9, 18
composite

11. Tell whether each number is prime or composite.
divisible by 1, 3, 9, 27
composite
B. 24
divisible by 1, 2, 3, 4, 6, 8, 12, 24
composite

12. 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.
divisible by 2, 4
divisible by 2, 3, 4, 5, 6, 9, 10
divisible by 3, 5
prime
composite