Factors of 315

How to find the factors of 315

Test every whole number from 1 up to the square root of 315 (√315 ≈ 17.748). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 315 ÷ 1 = 315 — so 1 and 315 are factors
• 315 ÷ 2 = 157.5 — not a whole number
• 315 ÷ 3 = 105 — so 3 and 105 are factors
• 315 ÷ 4 = 78.75 — not a whole number
• 315 ÷ 5 = 63 — so 5 and 63 are factors
• 315 ÷ 6 = 52.5 — not a whole number
• 315 ÷ 7 = 45 — so 7 and 45 are factors
• 315 ÷ 8 = 39.375 — not a whole number
• 315 ÷ 9 = 35 — so 9 and 35 are factors
• 315 ÷ 10 = 31.5 — not a whole number
• 315 ÷ 11 = 28.636 — not a whole number
• 315 ÷ 12 = 26.25 — not a whole number
• 315 ÷ 13 = 24.231 — not a whole number
• 315 ÷ 14 = 22.5 — not a whole number
• 315 ÷ 15 = 21 — so 15 and 21 are factors
• 315 ÷ 16 = 19.688 — not a whole number
• 315 ÷ 17 = 18.529 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105 and 315.

Prime factorization of 315

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

The primes you divided by give 315 = 3² × 5 × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) = 12.

Properties of 315

• 315 is a composite number.
• The sum of all its factors is 624; the sum of its proper factors (excluding 315) is 309, which makes it a deficient number (its proper factors add up to less than itself).
• 315 is not a perfect square, so its factors pair up evenly.
• Multiples of 315 include 630, 945, 1,260, 1,575 and so on.

Factors vs. multiples

Factors of 315 are the numbers that divide into it; multiples of 315 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.