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Whole Numbers Divisibility Rules

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Topics Whole Numbers Divisibility Rules

Divisibility by 3, 6, and 9

A number is divisible by 3 if its digits add up to a number divisible by 3. For example, 671,451 is divisible by 3 because 6 + 7 + 1 + 4 + 5 + 1 = 24, and 24 is divisible by 3. 84,950 is not divisible by 3, because 8 + 4 + 9 + 5 + 0 = 26, and 26 is not divisible by 3.

A number is divisible by 6 if it is divisible by 2 and 3. In other words, a number is divisible by 6 if its digits add up to a number divisible by 3 and it ends with an even number. 671,451 (our previous example) is divisible by 3, but not by 2, because 1 is not an even number. Therefore, 671,451 is not divisible by 6. On the other hand, 789,312 is divisible by 6, because 7 + 8 + 9 + 3 + 1 + 2 = 30, which is divisible by 3, and its last digit is 2, which is even.

A number is divisible by 9 if its digits add up to a number divisible by 9. For example, 91,458 is divisible by 9 because 9 + 1 + 4 + 5 + 8 = 27 and 27 is divisible by 9. 18,453 is not divisible by 9 because 1 + 8 + 4 + 5 + 3 = 21 and 21 is not divisible by 9.

Divisibility by 5

A number is divisible by 5 if it ends in 0 or 5. For example, 875 and 600 are divisible by 5, but 76,508 is not divisible by 5.

Divisibility by 10

A number is divisible by 10 if it ends in 0. For example, 65,110 and 90 are divisible by 10, but 6,007 is not divisible by 10.

Note: Because a number divided by itself always yields 1, a number is always divisible by itself. For example, 7 is divisible by 7 and 8,374 is divisible by 8,374.