1. Divisibility Rules and Mental Math

2. Vocabulary
A number is divisible by another number if it can be divided into and result in a remainder of 0.
24 is divisible by 4, because 24 ÷ 4 = 6.
24 is not divisible by 5, because 24 ÷ 5 = 4.8 (or 4R4).
An even number ends with a 0, 2, 4, 6, or 8.
An odd number ends with a 1, 3, 5, 7, or 9.

3. Divisibility Rules A number is divisible by…
2 if the ones digit is even.
3 if the sum of the digits are divisible by 3.
4 if the last 2 digits are divisible by 4.
5 if the ones digit is 0 or 5.

4. A number is divisible by…
6 if the number is divisible by BOTH 2 and 3.
9 if the sum of the digits are divisible by 9.
10 if the ones digit is 0.

5. Example: Test each number for divisibility by 3.
216
= 9
9 is divisible by 3, so 216 is divisible by 3.
yes
437
= 14
14 is not divisible by 3, so 437 is not divisible by 3. no

6. Example: Test the number for divisibility by 2, 5, or 10.
454,320
2 works because the number is even.
5 works because the number ends with 0.
10 works because the number ends with 0.
= 18.
Is the number divisible by 3 and9?
18 is divisible by 3 and 9, so 454,320 is also divisible by 3 and 9.