How to find the factors of 31
Test every whole number from 1 up to the square root of 31 (√31 ≈ 5.568). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 31 ÷ 1 = 31 — so 1 and 31 are factors
- 31 ÷ 2 = 15.5 — not a whole number
- 31 ÷ 3 = 10.333 — not a whole number
- 31 ÷ 4 = 7.75 — not a whole number
- 31 ÷ 5 = 6.2 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1 and 31.
Prime factorization of 31
31 is a prime number, so it cannot be broken down any further. Its prime factorization is simply 31.
Properties of 31
- 31 is a prime number.
- The sum of all its factors is 32; the sum of its proper factors (excluding 31) is 1, which makes it a deficient number (its proper factors add up to less than itself).
- 31 is not a perfect square, so its factors pair up evenly.
- Multiples of 31 include 62, 93, 124, 155 and so on.
Factors vs. multiples
Factors of 31 are the numbers that divide into it; multiples of 31 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.
Frequently asked questions
What are the factors of 31?
The factors of 31 are 1 and 31. Each of these divides 31 with no remainder.
How many factors does 31 have?
31 has 2 positive factors, which form 1 factor pair. Counting negative factors as well doubles that to 4.
What is the prime factorization of 31?
31 = 31. 31 is prime, so it is its own prime factorization.
Is 31 a prime number?
Yes. 31 is prime because its only factors are 1 and 31.