Check if a number is divisible by common integers and learn the rules.
Last updated: March 2026 | By ForgeCalc Engineering
Last digit is even
Sum of digits is divisible by 3
Last two digits are divisible by 4
Last digit is 0 or 5
Divisible by both 2 and 3
Double last digit and subtract from rest
Last three digits are divisible by 8
Sum of digits is divisible by 9
Ends in 0
Alternating sum of digits is divisible by 11
Divisible by both 3 and 4
Add 4 times last digit to rest
Divisibility tests are mental shortcuts that allow you to determine if a large number is divisible by a smaller one without performing long division. These rules are essential for simplifying fractions, finding prime factors, and modular arithmetic.
Most rules are based on the properties of our base-10 number system. For example, the rule for 3 and 9 works because 10 is 1 more than 9, meaning any power of 10 leaves a remainder of 1 when divided by 9 or 3.
Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is too. (e.g., 203: 20 - (3*2) = 14, which is 7*2).
Yes! For composite numbers like 6 (2*3) or 12 (3*4), a number is divisible if it passes the rules for its relatively prime factors.
Technically yes, but some rules (like for 17 or 19) are so complex that long division might actually be faster.
Because 10 ≡ 1 (mod 3). This means 100 ≡ 1, 1000 ≡ 1, and so on. Any number can be written as a sum of its digits multiplied by powers of 10, so the whole number is congruent to the sum of its digits.
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