Divisors of 512: All 10 Factors

Divisors (Factors) Calculator

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 512

The number 512 has 10 divisors:

1,  2,  4,  8,  16,  32,  64,  128,  256,  512

Divisor Pairs of 512

Each pair multiplies to 512:

Number of Divisors

The number 512 has 10 divisors, written as τ(512) = 10 in number theory.

Sum of Divisors

σ(512) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023

Prime Factorization of 512

See the full prime factorization calculator →

Properties of 512

• 512 is composite.
• 512 is not a perfect square.
• Number of divisors: 10.
• Sum of divisors: 1023.

Common Divisors with Another Number?

Looking for the divisors that 512 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 512

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √512 ≈ 22.63. If i divides 512, then both i and 512/i are divisors.

1. 1 divides 512 (512 ÷ 1 = 512) → pair (1, 512)
2. 2 divides 512 (512 ÷ 2 = 256) → pair (2, 256)
3. 4 divides 512 (512 ÷ 4 = 128) → pair (4, 128)
4. 8 divides 512 (512 ÷ 8 = 64) → pair (8, 64)
5. 16 divides 512 (512 ÷ 16 = 32) → pair (16, 32)
6. Collect all unique values: {1, 2, 4, 8, 16, 32, 64, 128, 256, 512} — total 10 divisors.
7. Sum: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023.

Nearby Examples

Related Operations for 512

• Multiples of 512 — "outward" complement; M is a multiple of 512 ⇔ 512 is a divisor of M
• 512 Prime Factorization — decompose into prime building blocks
• Find GCF of 512 and another number
• Find LCM of 512 and another number
• Is 512 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

Find all divisors of these numbers: