Factor Calculator

Factors of 512

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512. In total, 512 has 10 factors. Its prime factorization is 2⁹, and the sum of all its factors is 1023.

All factors of 512

Here are all 10 factors of 512, listed from smallest to largest.

1248163264128256512

Factor pairs of 512

These 5 pairs of whole numbers each multiply to give 512.

1 × 512 = 512
2 × 256 = 512
4 × 128 = 512
8 × 64 = 512
16 × 32 = 512

Prime factorization of 512

Dividing 512 by the smallest prime at each step gives its prime factorization:

512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Result: 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹

The distinct prime factors of 512 are 2. To factorize any other number, use the prime factorization calculator.

Factor tree of 512

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 51251222562128264232216282422
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 512

Number of factors10
Sum of factors1023
Sum of proper factors511
Prime factorization2⁹
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?Yes (8³)
ClassificationDeficient

What makes 512 interesting

  • 512 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 512 is a perfect cube: 8 × 8 × 8 = 512.
  • 512 is a deficient number: its proper factors sum to 511, which is 1 less than 512 itself.
  • 512 is a prime power: it is 2 raised to the power of 9. All of its factors are powers of 2.

How to find the factors of 512 yourself

Divide 512 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √512 ≈ 22.63, because every factor above that pairs with one below it.

512 ÷ 1 = 512 ✓
512 ÷ 2 = 256 ✓
512 ÷ 4 = 128 ✓
512 ÷ 8 = 64 ✓
512 ÷ 16 = 32 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. The factor calculator does this automatically for any number.

Numbers mathematically connected to 512.

Frequently asked questions about 512

What are the factors of 512?

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512. That is 10 factors in total, counting both 1 and 512.

Is 512 a prime number?

No, 512 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 512 is also divisible by 2.

What is the prime factorization of 512?

The prime factorization of 512 is 2⁹. Written out in full: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512. Its distinct prime factors are 2.

What two numbers multiply to give 512?

There are 5 pairs of whole numbers that multiply to 512: 1 × 512, 2 × 256, 4 × 128, 8 × 64, 16 × 32.

What is the sum of the factors of 512?

Adding all the factors of 512 together gives 1023. Excluding 512 itself, the proper factors sum to 511.

Is 512 a perfect square?

No, 512 is not a perfect square. There is no whole number that multiplies by itself to give 512. The nearest perfect squares are 484 and 529.

What is the largest factor of 512 other than itself?

The largest factor of 512 apart from 512 itself is 256, since 512 ÷ 256 = 2.

How many factors does 512 have?

512 has 10 factors: 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512. You can verify this from the prime factorization 2⁹: add 1 to each exponent and multiply, giving 10 = 10.

Explore more

Try another number in the factor calculator, break 512 down further with the prime factorization calculator, or compare 512 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.