Divisibility rules are simple ways to tell if one number can be divided evenly by another number. These rules help you decide quickly if a division problem will result in a whole number without doing the full calculation.
When a number is divisible by another number, the quotient is a whole number with no remainder.
A number is divisible by 2 if its last digit is even—meaning it ends in 0, 2, 4, 6, or 8.
All even numbers are divisible by 2. Odd numbers are not.
A number is divisible by 3 if the sum of its digits is divisible by 3.
If the sum of the digits is a multiple of 3 (like 3, 6, 9, 12, 15), then the whole number is divisible by 3.
A number is divisible by 4 if the last two digits form a number that is divisible by 4.
All numbers ending in 00, 04, 08, 12, 16, 20, and so on are divisible by 4.
A number is divisible by 5 if it ends in 0 or 5.
Every multiple of 5 will end in either 0 or 5.
A number is divisible by 6 if it is divisible by both 2 and 3.
If a number fails either the 2-rule or 3-rule, it is not divisible by 6.
A number is divisible by 7 if twice the last digit, subtracted from the rest of the number, gives a number that is divisible by 7.
The rule for 7 is trickier, so it helps to check by multiplying or dividing to confirm your answer.
A number is divisible by 8 if the last three digits form a number that is divisible by 8.
This rule works because 1,000 is divisible by 8, so only the last three digits matter.
A number is divisible by 9 if the sum of its digits is divisible by 9.
Divisibility by 9 works just like divisibility by 3 but uses 9 instead of 3 as the test number.
A number is divisible by 10 if it ends in 0.
Numbers divisible by 10 always have a 0 in the ones place because they are multiples of 10.
Divisibility rules help you solve real-world math problems quickly. You can use them to find equal groups, divide objects evenly, or simplify fractions without long division.
Before dividing, use divisibility rules to save time and confirm which numbers will divide evenly.