Factors of 507

How to find the factors of 507

Test every whole number from 1 up to the square root of 507 (√507 ≈ 22.517). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 507 ÷ 1 = 507 — so 1 and 507 are factors
• 507 ÷ 2 = 253.5 — not a whole number
• 507 ÷ 3 = 169 — so 3 and 169 are factors
• 507 ÷ 4 = 126.75 — not a whole number
• 507 ÷ 5 = 101.4 — not a whole number
• 507 ÷ 6 = 84.5 — not a whole number
• 507 ÷ 7 = 72.429 — not a whole number
• 507 ÷ 8 = 63.375 — not a whole number
• 507 ÷ 9 = 56.333 — not a whole number
• 507 ÷ 10 = 50.7 — not a whole number
• 507 ÷ 11 = 46.091 — not a whole number
• 507 ÷ 12 = 42.25 — not a whole number
• 507 ÷ 13 = 39 — so 13 and 39 are factors
• 507 ÷ 14 = 36.214 — not a whole number
• 507 ÷ 15 = 33.8 — not a whole number
• 507 ÷ 16 = 31.688 — not a whole number
• 507 ÷ 17 = 29.824 — not a whole number
• 507 ÷ 18 = 28.167 — not a whole number
• 507 ÷ 19 = 26.684 — not a whole number
• 507 ÷ 20 = 25.35 — not a whole number
• 507 ÷ 21 = 24.143 — not a whole number
• 507 ÷ 22 = 23.045 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 13, 39, 169 and 507.

Prime factorization of 507

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

The primes you divided by give 507 = 3 × 13². From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) = 6.

Properties of 507

• 507 is a composite number.
• The sum of all its factors is 732; the sum of its proper factors (excluding 507) is 225, which makes it a deficient number (its proper factors add up to less than itself).
• 507 is not a perfect square, so its factors pair up evenly.
• Multiples of 507 include 1,014, 1,521, 2,028, 2,535 and so on.

Factors vs. multiples

Factors of 507 are the numbers that divide into it; multiples of 507 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.