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Divisibility Rules for Prime Numbers

Divisibility rules help you guess possible factors accurately.

Divisibility Rules
Number is Divisible By If… Example
2 If the last digit is even (0,2,4,6, or 8), the number is divisible by 2.

216

Last digit:
6

Is 6 even?

Yes: 2 is a factor of 216.
3 If the sum of the digits is divisible by 3, the number is divisible by 3.

216

Sum of the digits:
2 + 1 + 6 = 9

Is 9 divisible by 3 with no remainder?
9 ÷ 3 = 3

Yes: 3 is a factor of 216.
5 If the last digit is a 5 or a 0, the number is divisible by 5.

216

Last digit:
6

Is 6 a 5 or 0?

No: 5 is not a factor of 216.
7 Multiply the last digit by 2.
Subtract the doubled last digit from the rest of the number.
If the answer is divisible by 7 (including 0), then so is the original number.

216

Last digit:
6

Double the last digit:
6 * 2 = 12

Subtract doubled last digit from 'rest of the number':
21 - 12 = 9

Is 9 divisible by 7 with no remainder?
9 ÷ 7=12/9

No. 7 is not a factor of 216.
11

Add the 1st, 3rd, 5th, 7th, (etc.) digits.
Add the 2nd, 4th, 6th, etc. digits.
If the difference of the two results, including 0, is divisible by 11, the number is divisible by 11.

825767855

Add 1st, 3rd, 5th, etc.:
8 + 5 + 6 + 8 + 5 = 32

Add 2nd, 4th, 6th, etc:
2 + 7 + 7 + 5 = 21

Is the difference divisible by 11 with no remainder?
32 - 21 = 11
11 ÷ 11 = 1

Yes: 11 is a factor of 825767855.
13

Multiply the last digit times 9.
Subtract the result (of 9 * the last digit) from the rest of the number.
If the difference is divisible by 13, so is the original number.

216

Last digit:
6

Multiply last digit by 9:
6 * 9 = 54

Subtract the product from the 'rest of the number':
21 - 54 = -33

Is -33 divisble by 13 with no remainder?
33 ÷ 13 = -25/33

No. 13 is not a factor of 216.

Vocabulary

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