Factors of 961

All factors of 961

Here are all 3 factors of 961, listed from smallest to largest.

Factor pairs of 961

These 2 pairs of whole numbers each multiply to give 961.

Notice the pair (31, 31) — because 961 is a perfect square, this pair uses the same number twice.

Prime factorization of 961

Dividing 961 by the smallest prime at each step gives its prime factorization:

The distinct prime factors of 961 are 31. To factorize any other number, use the prime factorization calculator.

Factor tree of 961

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

Properties of 961

What makes 961 interesting

• 961 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
• 961 is a perfect square: 31 × 31 = 961. This is why it has an odd number of factors (3) — the pair (31, 31) counts only once.
• 961 is a deficient number: its proper factors sum to 32, which is 929 less than 961 itself.
• 961 is a prime power: it is 31 raised to the power of 2. All of its factors are powers of 31.

How to find the factors of 961 yourself

Divide 961 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 √961 ≈ 31.00, because every factor above that pairs with one below it.

Reading both columns gives every factor: 1, 31, 961. The factor calculator does this automatically for any number.