Factors of 108

How to find the factors of 108

Test every whole number from 1 up to the square root of 108 (√108 ≈ 10.392). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 108 ÷ 1 = 108 — so 1 and 108 are factors
• 108 ÷ 2 = 54 — so 2 and 54 are factors
• 108 ÷ 3 = 36 — so 3 and 36 are factors
• 108 ÷ 4 = 27 — so 4 and 27 are factors
• 108 ÷ 5 = 21.6 — not a whole number
• 108 ÷ 6 = 18 — so 6 and 18 are factors
• 108 ÷ 7 = 15.429 — not a whole number
• 108 ÷ 8 = 13.5 — not a whole number
• 108 ÷ 9 = 12 — so 9 and 12 are factors
• 108 ÷ 10 = 10.8 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108.

Prime factorization of 108

Divide by the smallest prime that fits, and keep going until the quotient is 1:

The primes you divided by give 108 = 2² × 3³. From the exponents you can also count the factors without listing them: (2 + 1) × (3 + 1) = 12.

Properties of 108

• 108 is a composite number.
• The sum of all its factors is 280; the sum of its proper factors (excluding 108) is 172, which makes it a abundant number (its proper factors add up to more than itself).
• 108 is not a perfect square, so its factors pair up evenly.
• Multiples of 108 include 216, 324, 432, 540 and so on.

Factors vs. multiples

Factors of 108 are the numbers that divide into it; multiples of 108 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.