Factors of 512

How to find the factors of 512

Test every whole number from 1 up to the square root of 512 (√512 ≈ 22.627). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 512 ÷ 1 = 512 — so 1 and 512 are factors
• 512 ÷ 2 = 256 — so 2 and 256 are factors
• 512 ÷ 3 = 170.667 — not a whole number
• 512 ÷ 4 = 128 — so 4 and 128 are factors
• 512 ÷ 5 = 102.4 — not a whole number
• 512 ÷ 6 = 85.333 — not a whole number
• 512 ÷ 7 = 73.143 — not a whole number
• 512 ÷ 8 = 64 — so 8 and 64 are factors
• 512 ÷ 9 = 56.889 — not a whole number
• 512 ÷ 10 = 51.2 — not a whole number
• 512 ÷ 11 = 46.545 — not a whole number
• 512 ÷ 12 = 42.667 — not a whole number
• 512 ÷ 13 = 39.385 — not a whole number
• 512 ÷ 14 = 36.571 — not a whole number
• 512 ÷ 15 = 34.133 — not a whole number
• 512 ÷ 16 = 32 — so 16 and 32 are factors
• 512 ÷ 17 = 30.118 — not a whole number
• 512 ÷ 18 = 28.444 — not a whole number
• 512 ÷ 19 = 26.947 — not a whole number
• 512 ÷ 20 = 25.6 — not a whole number
• 512 ÷ 21 = 24.381 — not a whole number
• 512 ÷ 22 = 23.273 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512.

Prime factorization of 512

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

The primes you divided by give 512 = 2⁹. From the exponents you can also count the factors without listing them: (9 + 1) = 10.

Properties of 512

• 512 is a composite number.
• The sum of all its factors is 1,023; the sum of its proper factors (excluding 512) is 511, which makes it a deficient number (its proper factors add up to less than itself).
• 512 is not a perfect square, so its factors pair up evenly.
• 512 is also a perfect cube: 8³.
• Multiples of 512 include 1,024, 1,536, 2,048, 2,560 and so on.

Factors vs. multiples

Factors of 512 are the numbers that divide into it; multiples of 512 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.