Factors of 510

How to find the factors of 510

Test every whole number from 1 up to the square root of 510 (√510 ≈ 22.583). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 510 ÷ 1 = 510 — so 1 and 510 are factors
• 510 ÷ 2 = 255 — so 2 and 255 are factors
• 510 ÷ 3 = 170 — so 3 and 170 are factors
• 510 ÷ 4 = 127.5 — not a whole number
• 510 ÷ 5 = 102 — so 5 and 102 are factors
• 510 ÷ 6 = 85 — so 6 and 85 are factors
• 510 ÷ 7 = 72.857 — not a whole number
• 510 ÷ 8 = 63.75 — not a whole number
• 510 ÷ 9 = 56.667 — not a whole number
• 510 ÷ 10 = 51 — so 10 and 51 are factors
• 510 ÷ 11 = 46.364 — not a whole number
• 510 ÷ 12 = 42.5 — not a whole number
• 510 ÷ 13 = 39.231 — not a whole number
• 510 ÷ 14 = 36.429 — not a whole number
• 510 ÷ 15 = 34 — so 15 and 34 are factors
• 510 ÷ 16 = 31.875 — not a whole number
• 510 ÷ 17 = 30 — so 17 and 30 are factors
• 510 ÷ 18 = 28.333 — not a whole number
• 510 ÷ 19 = 26.842 — not a whole number
• 510 ÷ 20 = 25.5 — not a whole number
• 510 ÷ 21 = 24.286 — not a whole number
• 510 ÷ 22 = 23.182 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255 and 510.

Prime factorization of 510

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

The primes you divided by give 510 = 2 × 3 × 5 × 17. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 510

• 510 is a composite number.
• The sum of all its factors is 1,296; the sum of its proper factors (excluding 510) is 786, which makes it a abundant number (its proper factors add up to more than itself).
• 510 is not a perfect square, so its factors pair up evenly.
• Multiples of 510 include 1,020, 1,530, 2,040, 2,550 and so on.

Factors vs. multiples

Factors of 510 are the numbers that divide into it; multiples of 510 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.