Factor Calculator

Factors of 975

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975. In total, 975 has 12 factors. Its prime factorization is 3 × 5² × 13, and the sum of all its factors is 1736.

All factors of 975

Here are all 12 factors of 975, listed from smallest to largest.

135131525396575195325975

Factor pairs of 975

These 6 pairs of whole numbers each multiply to give 975.

1 × 975 = 975
3 × 325 = 975
5 × 195 = 975
13 × 75 = 975
15 × 65 = 975
25 × 39 = 975

Prime factorization of 975

Dividing 975 by the smallest prime at each step gives its prime factorization:

975 ÷ 3 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
Result: 975 = 3 × 5 × 5 × 13 = 3 × 5² × 13

The distinct prime factors of 975 are 3, 5, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 975

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

Factor tree of 9759753325565513
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 975

Number of factors12
Sum of factors1736
Sum of proper factors761
Prime factorization3 × 5² × 13
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 975 interesting

  • 975 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.
  • 975 is a deficient number: its proper factors sum to 761, which is 214 less than 975 itself.
  • 975 has 3 distinct prime factors (3, 5, 13), which is why it has so many divisors.

How to find the factors of 975 yourself

Divide 975 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 √975 ≈ 31.22, because every factor above that pairs with one below it.

975 ÷ 1 = 975 ✓
975 ÷ 3 = 325 ✓
975 ÷ 5 = 195 ✓
975 ÷ 13 = 75 ✓
975 ÷ 15 = 65 ✓
975 ÷ 25 = 39 ✓

Reading both columns gives every factor: 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975. The factor calculator does this automatically for any number.

Numbers mathematically connected to 975.

Frequently asked questions about 975

What are the factors of 975?

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975. That is 12 factors in total, counting both 1 and 975.

Is 975 a prime number?

No, 975 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 975 is also divisible by 3.

What is the prime factorization of 975?

The prime factorization of 975 is 3 × 5² × 13. Written out in full: 3 × 5 × 5 × 13 = 975. Its distinct prime factors are 3, 5, 13.

What two numbers multiply to give 975?

There are 6 pairs of whole numbers that multiply to 975: 1 × 975, 3 × 325, 5 × 195, 13 × 75, 15 × 65, 25 × 39.

What is the sum of the factors of 975?

Adding all the factors of 975 together gives 1736. Excluding 975 itself, the proper factors sum to 761.

Is 975 a perfect square?

No, 975 is not a perfect square. There is no whole number that multiplies by itself to give 975. The nearest perfect squares are 961 and 1024.

What is the largest factor of 975 other than itself?

The largest factor of 975 apart from 975 itself is 325, since 975 ÷ 325 = 3.

How many factors does 975 have?

975 has 12 factors: 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975. You can verify this from the prime factorization 3 × 5² × 13: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 975 down further with the prime factorization calculator, or compare 975 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.