Factor Calculator

Factors of 972

The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. In total, 972 has 18 factors. Its prime factorization is 2² × 3⁵, and the sum of all its factors is 2548.

All factors of 972

Here are all 18 factors of 972, listed from smallest to largest.

123469121827365481108162243324486972

Factor pairs of 972

These 9 pairs of whole numbers each multiply to give 972.

1 × 972 = 972
2 × 486 = 972
3 × 324 = 972
4 × 243 = 972
6 × 162 = 972
9 × 108 = 972
12 × 81 = 972
18 × 54 = 972
27 × 36 = 972

Prime factorization of 972

Dividing 972 by the smallest prime at each step gives its prime factorization:

972 ÷ 2 = 486
486 ÷ 2 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 972 = 2 × 2 × 3 × 3 × 3 × 3 × 3 = 2² × 3⁵

The distinct prime factors of 972 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 972

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

Factor tree of 972972248622433813273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 972

Number of factors18
Sum of factors2548
Sum of proper factors1576
Prime factorization2² × 3⁵
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 972 interesting

  • 972 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 9 different ways.
  • 972 is an abundant number: its proper factors sum to 1576, which is 604 more than 972 itself.

How to find the factors of 972 yourself

Divide 972 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 √97231.18, because every factor above that pairs with one below it.

972 ÷ 1 = 972
972 ÷ 2 = 486
972 ÷ 3 = 324
972 ÷ 4 = 243
972 ÷ 6 = 162
972 ÷ 9 = 108
972 ÷ 12 = 81
972 ÷ 18 = 54
972 ÷ 27 = 36

Reading both columns gives every factor: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. The factor calculator does this automatically for any number.

Frequently asked questions about 972

What are the factors of 972?

The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. That is 18 factors in total, counting both 1 and 972.

Is 972 a prime number?

No, 972 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 972 is also divisible by 2.

What is the prime factorization of 972?

The prime factorization of 972 is 2² × 3⁵. Written out in full: 2 × 2 × 3 × 3 × 3 × 3 × 3 = 972. Its distinct prime factors are 2, 3.

What two numbers multiply to give 972?

There are 9 pairs of whole numbers that multiply to 972: 1 × 972, 2 × 486, 3 × 324, 4 × 243, 6 × 162, 9 × 108, 12 × 81, 18 × 54, 27 × 36.

What is the sum of the factors of 972?

Adding all the factors of 972 together gives 2548. Excluding 972 itself, the proper factors sum to 1576.

Is 972 a perfect square?

No, 972 is not a perfect square. There is no whole number that multiplies by itself to give 972. The nearest perfect squares are 961 and 1024.

What is the largest factor of 972 other than itself?

The largest factor of 972 apart from 972 itself is 486, since 972 ÷ 486 = 2.

How many factors does 972 have?

972 has 18 factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972. You can verify this from the prime factorization 2² × 3⁵: add 1 to each exponent and multiply, giving 3 × 6 = 18.

Explore more

Try another number in the factor calculator, break 972 down further with the prime factorization calculator, or compare 972 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.