Factors of 72
There are 12 factors of 72 — the full list is below, with factor pairs, prime factorization, and divisibility notes.
Factors of 72
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factor pairs of 72
- 1 × 72
- 2 × 36
- 3 × 24
- 4 × 18
- 6 × 12
- 8 × 9
Prime factorization of 72
72 = 2³ × 3²
Number facts
- 72 is a composite number.
- 72 has 12 factors.
- 72 is not a perfect square.
- The sum of all factors of 72 is 195.
Divisibility rules that apply to 72
- 72 is divisible by 2 because it ends in an even digit (0, 2, 4, 6, or 8).
- 72 is divisible by 3 because the sum of its digits (9) is divisible by 3.
- 72 is divisible by 9 because the sum of its digits (9) is divisible by 9.
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How the factors of 72 are calculated
To find the factors of 72, every whole number from 1 up to the square root of 72(about 8.49) is tested for even division. 72 is even, and it divides evenly by 2, 3, 4, 6, among others. Written as a product of primes, 72 = 2³ × 3², which confirms every factor above is a combination of those prime building blocks.
Frequently asked questions about 72
How many factors does 72 have?
72 has 12 factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Is 72 a prime number?
No. 72 is composite because it has factors other than 1 and itself.
What are the factor pairs of 72?
The factor pairs of 72 are 1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9.
What is the prime factorization of 72?
The prime factorization of 72 is 2³ × 3².