# Divisibility Rules and Mental Math

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Divisibility Rules and Mental Math

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.

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.

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.

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

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.