How to Calculate Divisibility
What is Divisibility?
Divisibility rules are shortcuts to determine whether one number is divisible by another without performing full division. They're used in mental arithmetic, number theory, and primality testing.
Formula
Various rules: ÷2 (even), ÷3 (digit sum), ÷5 (ends 0 or 5), ÷9 (digit sum), etc.
- n
- the number being tested
- d
- the divisor (2, 3, 5, 7, 11, etc.)
Step-by-Step Guide
- 1÷2: last digit even
- 2÷3: sum of digits divisible by 3
- 3÷4: last two digits form number divisible by 4
- 4÷5: last digit is 0 or 5
- 5÷9: sum of digits divisible by 9
Worked Examples
Input
360
Result
Divisible by 2,3,4,5,6,8,9,10,12
Input
1001
Result
Divisible by 7 and 11 (and 13)
Frequently Asked Questions
What is the divisibility rule for 7?
One method: remove the last digit, double it, and subtract from the remaining number. Repeat until a known multiple.
What is the divisibility rule for 11?
Alternately subtract and add digits from right to left. If the result is divisible by 11, so is the original.
Are divisibility rules faster than actual division?
Yes, for quick mental checks. But for programming, direct modulo might be faster.
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