Factor Calculator

Factors of 72

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. In total, 72 has 12 factors. Its prime factorization is 2³ × 3², and the sum of all its factors is 195.

All factors of 72

Here are all 12 factors of 72, listed from smallest to largest.

12346891218243672

Factor pairs of 72

These 6 pairs of whole numbers each multiply to give 72.

1 × 72 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 × 12 = 72
8 × 9 = 72

Prime factorization of 72

Dividing 72 by the smallest prime at each step gives its prime factorization:

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

The distinct prime factors of 72 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 72

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 72722362182933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 72

Number of factors12
Sum of factors195
Sum of proper factors123
Prime factorization2³ × 3²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 72 interesting

  • 72 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 72 is an abundant number: its proper factors sum to 123, which is 51 more than 72 itself.

How to find the factors of 72 yourself

Divide 72 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √72 ≈ 8.49, because every factor above that pairs with one below it.

72 ÷ 1 = 72 ✓
72 ÷ 2 = 36 ✓
72 ÷ 3 = 24 ✓
72 ÷ 4 = 18 ✓
72 ÷ 6 = 12 ✓
72 ÷ 8 = 9 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. The factor calculator does this automatically for any number.

Numbers mathematically connected to 72.

Frequently asked questions about 72

What are the factors of 72?

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. That is 12 factors in total, counting both 1 and 72.

Is 72 a prime number?

No, 72 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 72 is also divisible by 2.

What is the prime factorization of 72?

The prime factorization of 72 is 2³ × 3². Written out in full: 2 × 2 × 2 × 3 × 3 = 72. Its distinct prime factors are 2, 3.

What two numbers multiply to give 72?

There are 6 pairs of whole numbers that multiply to 72: 1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9.

What is the sum of the factors of 72?

Adding all the factors of 72 together gives 195. Excluding 72 itself, the proper factors sum to 123.

Is 72 a perfect square?

No, 72 is not a perfect square. There is no whole number that multiplies by itself to give 72. The nearest perfect squares are 64 and 81.

What is the largest factor of 72 other than itself?

The largest factor of 72 apart from 72 itself is 36, since 72 ÷ 36 = 2.

How many factors does 72 have?

72 has 12 factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. You can verify this from the prime factorization 2³ × 3²: add 1 to each exponent and multiply, giving 4 × 3 = 12.

Explore more

Try another number in the factor calculator, break 72 down further with the prime factorization calculator, or compare 72 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.