How to find the factors of 107
Test every whole number from 1 up to the square root of 107 (√107 ≈ 10.344). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 107 ÷ 1 = 107 — so 1 and 107 are factors
- 107 ÷ 2 = 53.5 — not a whole number
- 107 ÷ 3 = 35.667 — not a whole number
- 107 ÷ 4 = 26.75 — not a whole number
- 107 ÷ 5 = 21.4 — not a whole number
- 107 ÷ 6 = 17.833 — not a whole number
- 107 ÷ 7 = 15.286 — not a whole number
- 107 ÷ 8 = 13.375 — not a whole number
- 107 ÷ 9 = 11.889 — not a whole number
- 107 ÷ 10 = 10.7 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1 and 107.
Prime factorization of 107
107 is a prime number, so it cannot be broken down any further. Its prime factorization is simply 107.
Properties of 107
- 107 is a prime number.
- The sum of all its factors is 108; the sum of its proper factors (excluding 107) is 1, which makes it a deficient number (its proper factors add up to less than itself).
- 107 is not a perfect square, so its factors pair up evenly.
- Multiples of 107 include 214, 321, 428, 535 and so on.
Factors vs. multiples
Factors of 107 are the numbers that divide into it; multiples of 107 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 107?
The factors of 107 are 1 and 107. Each of these divides 107 with no remainder.
How many factors does 107 have?
107 has 2 positive factors, which form 1 factor pair. Counting negative factors as well doubles that to 4.
What is the prime factorization of 107?
107 = 107. 107 is prime, so it is its own prime factorization.
Is 107 a prime number?
Yes. 107 is prime because its only factors are 1 and 107.