How to find the factors of 109
Test every whole number from 1 up to the square root of 109 (√109 ≈ 10.440). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 109 ÷ 1 = 109 — so 1 and 109 are factors
- 109 ÷ 2 = 54.5 — not a whole number
- 109 ÷ 3 = 36.333 — not a whole number
- 109 ÷ 4 = 27.25 — not a whole number
- 109 ÷ 5 = 21.8 — not a whole number
- 109 ÷ 6 = 18.167 — not a whole number
- 109 ÷ 7 = 15.571 — not a whole number
- 109 ÷ 8 = 13.625 — not a whole number
- 109 ÷ 9 = 12.111 — not a whole number
- 109 ÷ 10 = 10.9 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1 and 109.
Prime factorization of 109
109 is a prime number, so it cannot be broken down any further. Its prime factorization is simply 109.
Properties of 109
- 109 is a prime number.
- The sum of all its factors is 110; the sum of its proper factors (excluding 109) is 1, which makes it a deficient number (its proper factors add up to less than itself).
- 109 is not a perfect square, so its factors pair up evenly.
- Multiples of 109 include 218, 327, 436, 545 and so on.
Factors vs. multiples
Factors of 109 are the numbers that divide into it; multiples of 109 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 109?
The factors of 109 are 1 and 109. Each of these divides 109 with no remainder.
How many factors does 109 have?
109 has 2 positive factors, which form 1 factor pair. Counting negative factors as well doubles that to 4.
What is the prime factorization of 109?
109 = 109. 109 is prime, so it is its own prime factorization.
Is 109 a prime number?
Yes. 109 is prime because its only factors are 1 and 109.