Definition
Divisibility rule
A divisibility rule is a digit or place-value test that tells whether one whole number divides another with no remainder.
What it means
Each rule belongs to a particular divisor. Check the digits the rule names. If the condition is true, the number can be split into equal groups of that size with nothing left. The rule works because of base-ten place value, not because the digits merely look patterned.
Remember it
Name the divisor, check its digit rule, then predict zero remainder.
Example
Is 7,452 divisible by 3? Add its digits: 7 + 4 + 5 + 2 = 18. Since 18 is divisible by 3, 7,452 is divisible by 3; in fact, 7,452 ÷ 3 = 2,484.
Watch for
A number ending in 5 passes the rule for 5, but that ending alone says nothing about divisibility by 3.
Common mix-up
A divisibility rule predicts whether division is exact; it does not usually tell you the quotient.
Exact meaning
For a chosen nonzero whole-number divisor, a divisibility rule is a condition on an integer’s base-ten digits that is equivalent to divisibility by that divisor, so exact divisibility can be decided without completing the quotient calculation.