Divisibility Tests

We use the notation a/b to say “a divides b”. For example, 2/10 would tell us that “2 divides 10”.

Divisibility by two: If the last digit is even, the original number is divisible by 2.
Example that works 314
Example that doesn’t work 413

Divisibility by three: If the sum of the digits is divisible by 3, then the original number is divisible by 3.
Example that works 315
Example that doesn’t work 314

Divisibility by four: If the last two digits form a number that is divisible by 4, then the original number is divisible by 5.
Example that works 316
Example that doesn’t work 315

Divisibility by five:  If the last digit is either a 0 or 5, then the original number is divisible by 5.
Example that works 320
Example that doesn’t work 513

Divisibility by six:  If the number is divisible by 2 and 3, then it is divisible by 6.
Example that works 414
Example that doesn’t work 314

Divisibility by seven: Doesn’t work. Just preform the division.

Divisibility by eight: if the last three digits form a number that is divisible by 8, then the original number is divisible by 9.
Example that works 1096
Example that doesn’t work 403316

Divisibility by nine: If the sum of the digits is divisible by 9, then the original number is divisible by 9.
Example that works 315
Example that doesn’t work 317

Divisibility by ten: If the last digit is 0, then the original number is divisible by ten.
Example that works 520
Example that doesn’t work 523

Divisibility by eleven: Find the sum of the odd-numbered digits (odd sum) and the sum of the even numbered digits (even sum). Take the difference between odd sum and even sum. If this difference is divisible by 11, then the original number is divisible by 11.

Divisibility by twelve: If the number is divisible by 3 and 4, then it is divisible by 12.
Example that works 1308
Example that doesn’t 1433

 

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