Factors of 361

All factors of 361

Here are all 3 factors of 361, listed from smallest to largest.

Factor pairs of 361

These 2 pairs of whole numbers each multiply to give 361.

Notice the pair (19, 19) — because 361 is a perfect square, this pair uses the same number twice.

Prime factorization of 361

Dividing 361 by the smallest prime at each step gives its prime factorization:

The distinct prime factors of 361 are 19. To factorize any other number, use the prime factorization calculator.

Factor tree of 361

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

Properties of 361

What makes 361 interesting

• 361 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.
• 361 is a perfect square: 19 × 19 = 361. This is why it has an odd number of factors (3) — the pair (19, 19) counts only once.
• 361 is a deficient number: its proper factors sum to 20, which is 341 less than 361 itself.
• 361 is a prime power: it is 19 raised to the power of 2. All of its factors are powers of 19.

How to find the factors of 361 yourself

Divide 361 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 √361 ≈ 19.00, because every factor above that pairs with one below it.

Reading both columns gives every factor: 1, 19, 361. The factor calculator does this automatically for any number.