Divisibility Calculator — Check Divisibility Rules
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Custom Divisor Result
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Understanding Divisibility Rules
Divisibility rules are shortcuts to check if a number divides evenly without performing long division. For example, a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, and by 5 if it ends in 0 or 5.
More rules: divisible by 4 if the last two digits form a number divisible by 4, by 6 if divisible by both 2 and 3, by 8 if the last three digits are divisible by 8, by 9 if the digit sum is divisible by 9, and by 11 if the alternating sum of digits is divisible by 11.
These rules are useful for mental math, simplifying fractions, and checking arithmetic. This calculator tests divisibility by 2 through 12 and any custom divisor you enter, showing which rules apply to your number.
Frequently Asked Questions
What is the divisibility rule for 7?
Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, so is the original. For 364: 36 - 2(4) = 28, which is divisible by 7, so 364 is too.
How do you check divisibility by 11?
Compute the alternating sum of digits (add odd-position digits, subtract even-position digits). If the result is divisible by 11, the original number is too. For 918082: 9-1+8-0+8-2 = 22, divisible by 11.
Why are divisibility rules useful?
They allow quick mental checks without calculators, help simplify fractions, verify arithmetic, and are foundational for number theory and cryptography.