Divisibility Rules

Integer Properties

Lesson by Mike McGarry

Magoosh Expert

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Multiples

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Lesson by Mike McGarry

Magoosh Expert

Summary

ACT divisibility questions become much faster when you combine strong multiplication-table recall with a small set of standard divisibility rules. The key rules focus on checking the last digit, the last two digits, or the sum of the digits to determine divisibility without long division.

Basic divisibility questions such as whether 56 is divisible by 7 or 50 is divisible by 13 should be answered quickly from memorized multiplication facts, so solid times-table fluency is essential.
Divisibility by 2 and 5 depends only on the ones digit: even last digits mean divisibility by 2, and a last digit of 0 or 5 means divisibility by 5.
Divisibility by 4 depends on the last two digits: if the two-digit ending is divisible by 4, then the entire number is divisible by 4.
Divisibility by 3 is determined by adding all digits; if that sum is divisible by 3, then the whole number is divisible by 3, which works for both small and very large numbers.
Divisibility by 9 uses the same digit-sum method as 3, but the sum itself must be divisible by 9; this also helps distinguish numbers divisible by 3 from those divisible by 9.
Divisibility by 6 combines rules: a number must be divisible by both 2 and 3, so checking evenness and then checking the digit sum gives the answer efficiently.

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