Name
class
date
Divisibility Rules
You can use divisibility tests to simplify fractions. One number is divisible by another if the
remainder is zero.
Number
2
3
5
6
9
10
Divisibility Test
The ones digit is 0, 2, 4, 6, or 8.
The sum of the digits is divisible by 3.
The ones digit is 0 or 5.
The number is divisible by both 2 and 3.
The sum of the digits is divisible by 9.
The ones digit is 0.
EXAMPLE
Determine if the number 2,145 is divisible by 2, 3, 5, 6, 9 or 10.
Step 1: Is the number divisible by 2?
No, the number is NOT even, and therefore not
divisible by 2.
Step 4: Is the number divisible by 6?
No, the number is NOT divisible by both 2 and 3.
Step 5: Is the number divisible by 9?
The sum of the digits is 2 + 1 + 4 + 5 = 12.
12 is NOT divisible by 9; so 2,145 is divisible by 9.
Step 2: Is the number divisible by 3?
The sum of the digits is 2 + 1 + 4 + 5 = 12.
12 is divisible by 3; so 2,145 is divisible by 3.
Step 6: Is the number divisible by 10?
No, the last digit is not a 0.
Step 3: Is the number divisible by 5?
Yes, the last digit is a 5.
Solution: The number 2,145 is divisible by 3, 5, and 9.
Practice
Determine whether each number is divisible by 2, 3, 5, 6, 9 or 10.
2
3
5
6
9
10
76
124
390
1,024
1,275
34,776
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SpringBoard Course 1, Unit 1