Divisibility Rules: Quick Tricks for 2 to 11

Divisibility rules let you check if a number divides evenly without doing the division. They're the secret to fast factoring, simplifying and prime testing.

Here are the most useful rules from 2 to 11.

The everyday rules (2, 5, 10)

• 2: last digit is even.
• 5: ends in 0 or 5.
• 10: ends in 0.

Digit-sum rules (3 and 9)

• 3: the digit sum is a multiple of 3 (e.g. 123 → 1+2+3 = 6 ✓).
• 9: the digit sum is a multiple of 9.

Power-of-two rules (4 and 8)

• 4: the last two digits form a multiple of 4.
• 8: the last three digits form a multiple of 8.

The trickier ones (6, 7, 11)

• 6: divisible by both 2 and 3.
• 7: double the last digit, subtract from the rest; if the result is a multiple of 7, so is the number.
• 11: alternating digit sum is a multiple of 11.

Putting them to work

Use these to find the smallest prime factor fast, then confirm with the Prime Factorization Calculator or Prime Number Checker.