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.
Factor pairs of 972
These 9 pairs of whole numbers each multiply to give 972.
Prime factorization of 972
Dividing 972 by the smallest prime at each step gives its prime factorization:
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.
Properties of 972
| Number of factors | 18 |
|---|---|
| Sum of factors | 2548 |
| Sum of proper factors | 1576 |
| Prime factorization | 2² × 3⁵ |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | No |
| Perfect cube? | No |
| Classification | Abundant |
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 √972 ≈ 31.18, because every factor above that pairs with one below it.
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.
Related numbers
Numbers mathematically connected to 972.
Frequently asked questions about 972
What are the factors of 972?
Is 972 a prime number?
What is the prime factorization of 972?
What two numbers multiply to give 972?
What is the sum of the factors of 972?
Is 972 a perfect square?
What is the largest factor of 972 other than itself?
How many factors does 972 have?
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.