# Divisibility Rules for the First Five Prime Numbers as well as 0 and 1

0 - No number is divisible by 0.

1 - Every number is divisible by 1. That is why 1 is called the multiplicative identity (any number divided by 1 equals itself).

2 - Every even number is divisible by 2. Even numbers are numbers that end in either 0, 2, 4, 6, or 8.

3 - The sum of the digits in the number must equal a number divisible by 3. If unsure whether the sum obtained is a number divisible by 3, keep repeating the process with the new number until certainty is attained. For example, the number 342 is divisible by 3 because 3 + 4 + 2 = 9 and 9 is divisible by 3. 124 is not divisible by three because 1 + 2 + 4 = 7 and 7 is not divisible by 3.

5 - The number must end in either 0 or 5.

7 - Take the last digit in the number, double it and subtract it from the rest of the number. If the result is a number divisible by 7, then the number is also divisible by 7. If unsure whether the result obtained is divisible by 7, keep repeating the process until certainty is attained. For example, the number 54726 is divisible by 7 because 5472 - 12 (6 doubled) = 5460

546 - 0 = 546

54 - 12 = 42

I know that 42 is divisible by 7, therefore so is 54726. The number 8751 is not divisible by 7 because 875 - 2 = 873

87 - 6 = 81

8 - 2 = 6

Since 6 is not divisible by 7, neither is 8751.

11 - Starting with the first digit of the number, add every other digit in the number. Subtract that result from the sum of the remaining digits. If the result (ignoring the sign) is a number divisible by 11, then the number is also divisible by 11. Like the divisibility rule for 7, this process may be repeated until certainty that the result is divisible by 11 is attained.

For example, the number 845196 is divisible by 11 because (8 + 5 + 9) - (4 + 1 + 6) = 22 - 11 = 11 Since 11 is divisible by 11, then so is 845196.

The number 55529 is not divisible by 11 because (5 + 5 + 9) - (5 + 2) = 19 - 7 = 12

Since 12 is not divisible by 11, then neither is 55529.

### Comments

Zero is not divisible by any number. That's interesting. I know that no number is divisible by 0, but I always thought that 0 was divisible by all other numbers. To wit 0/5 = 0 0/1 = 0 0/136,567 = 0 I suppose, philosophically speaking, if something is divisible by everything, maybe it's divisible by nothing.
Thanks Scott for correcting me. I meant to say that nothing is divisible by zero. I will correct the blog right now.

\$30p/h

Bruno T.

Math Tutor and Former Supplemental Instruction Leader

20+ hours

## Stuck?

Find the perfect tutor and raise your grades.

### New York Algebra Tutors

if (isMyPost) { }