Factors of 312

How to find the factors of 312

Test every whole number from 1 up to the square root of 312 (√312 ≈ 17.664). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 312 ÷ 1 = 312 — so 1 and 312 are factors
• 312 ÷ 2 = 156 — so 2 and 156 are factors
• 312 ÷ 3 = 104 — so 3 and 104 are factors
• 312 ÷ 4 = 78 — so 4 and 78 are factors
• 312 ÷ 5 = 62.4 — not a whole number
• 312 ÷ 6 = 52 — so 6 and 52 are factors
• 312 ÷ 7 = 44.571 — not a whole number
• 312 ÷ 8 = 39 — so 8 and 39 are factors
• 312 ÷ 9 = 34.667 — not a whole number
• 312 ÷ 10 = 31.2 — not a whole number
• 312 ÷ 11 = 28.364 — not a whole number
• 312 ÷ 12 = 26 — so 12 and 26 are factors
• 312 ÷ 13 = 24 — so 13 and 24 are factors
• 312 ÷ 14 = 22.286 — not a whole number
• 312 ÷ 15 = 20.8 — not a whole number
• 312 ÷ 16 = 19.5 — not a whole number
• 312 ÷ 17 = 18.353 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156 and 312.

Prime factorization of 312

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

The primes you divided by give 312 = 2³ × 3 × 13. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 312

• 312 is a composite number.
• The sum of all its factors is 840; the sum of its proper factors (excluding 312) is 528, which makes it a abundant number (its proper factors add up to more than itself).
• 312 is not a perfect square, so its factors pair up evenly.
• Multiples of 312 include 624, 936, 1,248, 1,560 and so on.

Factors vs. multiples

Factors of 312 are the numbers that divide into it; multiples of 312 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.