Factor Calculator

Factors of 31

The factors of 31 are 1 and 31. Since 31 is a prime number, it has exactly 2 factors and cannot be divided evenly by any other whole number. The sum of its factors is 32, and its prime factorization is simply 31 itself.

All factors of 31

Here are all 2 factors of 31, listed from smallest to largest.

131

Factor pairs of 31

There is only one factor pair for 31, because it is prime.

1 × 31 = 31

Prime factorization of 31

31 is a prime number, so it cannot be broken down further. Its prime factorization is simply 31.

Properties of 31

Number of factors2
Sum of factors32
Sum of proper factors1
Prime factorization31
Prime or composite?Prime
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 31 interesting

  • 31 is a prime number, so its only factors are 1 and 31. It cannot be split into a product of two smaller whole numbers.
  • Every prime number is deficient — the sum of its proper factors is always 1, which is far less than the number itself.

How to find the factors of 31 yourself

Divide 31 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 √31 ≈ 5.57, because every factor above that pairs with one below it.

31 ÷ 1 = 31 ✓

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

Numbers mathematically connected to 31.

Frequently asked questions about 31

What are the factors of 31?

The factors of 31 are 1 and 31. That is 2 factors in total, counting both 1 and 31.

Is 31 a prime number?

Yes, 31 is a prime number. It has exactly two factors: 1 and 31. No other whole number divides it evenly.

What is the prime factorization of 31?

31 is already prime, so its prime factorization is simply 31. It cannot be broken down any further.

What two numbers multiply to give 31?

There is 1 pair of whole numbers that multiply to 31: 1 × 31.

What is the sum of the factors of 31?

Adding all the factors of 31 together gives 32. Excluding 31 itself, the proper factors sum to 1.

Is 31 a perfect square?

No, 31 is not a perfect square. There is no whole number that multiplies by itself to give 31. The nearest perfect squares are 25 and 36.

What is the largest factor of 31 other than itself?

The largest factor of 31 apart from 31 itself is 1, since 31 ÷ 1 = 31.

How many factors does 31 have?

31 has 2 factors: 1 and 31.

Explore more

Try another number in the factor calculator, break 31 down further with the prime factorization calculator, or compare 31 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.