Factors of 117

How to find the factors of 117

Test every whole number from 1 up to the square root of 117 (√117 ≈ 10.817). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 117 ÷ 1 = 117 — so 1 and 117 are factors
• 117 ÷ 2 = 58.5 — not a whole number
• 117 ÷ 3 = 39 — so 3 and 39 are factors
• 117 ÷ 4 = 29.25 — not a whole number
• 117 ÷ 5 = 23.4 — not a whole number
• 117 ÷ 6 = 19.5 — not a whole number
• 117 ÷ 7 = 16.714 — not a whole number
• 117 ÷ 8 = 14.625 — not a whole number
• 117 ÷ 9 = 13 — so 9 and 13 are factors
• 117 ÷ 10 = 11.7 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 13, 39 and 117.

Prime factorization of 117

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

The primes you divided by give 117 = 3² × 13. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.

Properties of 117

• 117 is a composite number.
• The sum of all its factors is 182; the sum of its proper factors (excluding 117) is 65, which makes it a deficient number (its proper factors add up to less than itself).
• 117 is not a perfect square, so its factors pair up evenly.
• Multiples of 117 include 234, 351, 468, 585 and so on.

Factors vs. multiples

Factors of 117 are the numbers that divide into it; multiples of 117 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.