Factors of 256

How to find the factors of 256

Test every whole number from 1 up to the square root of 256 (√256 ≈ 16.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 256 ÷ 1 = 256 — so 1 and 256 are factors
• 256 ÷ 2 = 128 — so 2 and 128 are factors
• 256 ÷ 3 = 85.333 — not a whole number
• 256 ÷ 4 = 64 — so 4 and 64 are factors
• 256 ÷ 5 = 51.2 — not a whole number
• 256 ÷ 6 = 42.667 — not a whole number
• 256 ÷ 7 = 36.571 — not a whole number
• 256 ÷ 8 = 32 — so 8 and 32 are factors
• 256 ÷ 9 = 28.444 — not a whole number
• 256 ÷ 10 = 25.6 — not a whole number
• 256 ÷ 11 = 23.273 — not a whole number
• 256 ÷ 12 = 21.333 — not a whole number
• 256 ÷ 13 = 19.692 — not a whole number
• 256 ÷ 14 = 18.286 — not a whole number
• 256 ÷ 15 = 17.067 — not a whole number
• 256 ÷ 16 = 16 — so 16 and 16 are factors

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

Prime factorization of 256

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

The primes you divided by give 256 = 2⁸. From the exponents you can also count the factors without listing them: (8 + 1) = 9.

Properties of 256

• 256 is a composite number.
• The sum of all its factors is 511; the sum of its proper factors (excluding 256) is 255, which makes it a deficient number (its proper factors add up to less than itself).
• 256 is a perfect square: 16 × 16. Perfect squares always have an odd number of factors.
• Multiples of 256 include 512, 768, 1,024, 1,280 and so on.

Factors vs. multiples

Factors of 256 are the numbers that divide into it; multiples of 256 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.