Factors of 513

How to find the factors of 513

Test every whole number from 1 up to the square root of 513 (√513 ≈ 22.650). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 513 ÷ 1 = 513 — so 1 and 513 are factors
• 513 ÷ 2 = 256.5 — not a whole number
• 513 ÷ 3 = 171 — so 3 and 171 are factors
• 513 ÷ 4 = 128.25 — not a whole number
• 513 ÷ 5 = 102.6 — not a whole number
• 513 ÷ 6 = 85.5 — not a whole number
• 513 ÷ 7 = 73.286 — not a whole number
• 513 ÷ 8 = 64.125 — not a whole number
• 513 ÷ 9 = 57 — so 9 and 57 are factors
• 513 ÷ 10 = 51.3 — not a whole number
• 513 ÷ 11 = 46.636 — not a whole number
• 513 ÷ 12 = 42.75 — not a whole number
• 513 ÷ 13 = 39.462 — not a whole number
• 513 ÷ 14 = 36.643 — not a whole number
• 513 ÷ 15 = 34.2 — not a whole number
• 513 ÷ 16 = 32.063 — not a whole number
• 513 ÷ 17 = 30.176 — not a whole number
• 513 ÷ 18 = 28.5 — not a whole number
• 513 ÷ 19 = 27 — so 19 and 27 are factors
• 513 ÷ 20 = 25.65 — not a whole number
• 513 ÷ 21 = 24.429 — not a whole number
• 513 ÷ 22 = 23.318 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 9, 19, 27, 57, 171 and 513.

Prime factorization of 513

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

The primes you divided by give 513 = 3³ × 19. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) = 8.

Properties of 513

• 513 is a composite number.
• The sum of all its factors is 800; the sum of its proper factors (excluding 513) is 287, which makes it a deficient number (its proper factors add up to less than itself).
• 513 is not a perfect square, so its factors pair up evenly.
• Multiples of 513 include 1,026, 1,539, 2,052, 2,565 and so on.

Factors vs. multiples

Factors of 513 are the numbers that divide into it; multiples of 513 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.