Factor Calculator

Factors of 864

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864. In total, 864 has 24 factors. Its prime factorization is 2⁵ × 3³, and the sum of all its factors is 2520.

All factors of 864

Here are all 24 factors of 864, listed from smallest to largest.

12346891216182427323648547296108144216288432864

Factor pairs of 864

These 12 pairs of whole numbers each multiply to give 864.

1 × 864 = 864
2 × 432 = 864
3 × 288 = 864
4 × 216 = 864
6 × 144 = 864
8 × 108 = 864
9 × 96 = 864
12 × 72 = 864
16 × 54 = 864
18 × 48 = 864
24 × 36 = 864
27 × 32 = 864

Prime factorization of 864

Dividing 864 by the smallest prime at each step gives its prime factorization:

864 ÷ 2 = 432
432 ÷ 2 = 216
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁵ × 3³

The distinct prime factors of 864 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 864

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

Factor tree of 8648642432221621082542273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 864

Number of factors24
Sum of factors2520
Sum of proper factors1656
Prime factorization2⁵ × 3³
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 864 interesting

  • 864 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
  • 864 is an abundant number: its proper factors sum to 1656, which is 792 more than 864 itself.

How to find the factors of 864 yourself

Divide 864 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 √864 ≈ 29.39, because every factor above that pairs with one below it.

864 ÷ 1 = 864 ✓
864 ÷ 2 = 432 ✓
864 ÷ 3 = 288 ✓
864 ÷ 4 = 216 ✓
864 ÷ 6 = 144 ✓
864 ÷ 8 = 108 ✓
864 ÷ 9 = 96 ✓
864 ÷ 12 = 72 ✓
864 ÷ 16 = 54 ✓
864 ÷ 18 = 48 ✓
864 ÷ 24 = 36 ✓
864 ÷ 27 = 32 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. The factor calculator does this automatically for any number.

Numbers mathematically connected to 864.

Frequently asked questions about 864

What are the factors of 864?

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864. That is 24 factors in total, counting both 1 and 864.

Is 864 a prime number?

No, 864 is not prime — it is a composite number with 24 factors. A prime number has exactly two factors, but 864 is also divisible by 2.

What is the prime factorization of 864?

The prime factorization of 864 is 2⁵ × 3³. Written out in full: 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 864. Its distinct prime factors are 2, 3.

What two numbers multiply to give 864?

There are 12 pairs of whole numbers that multiply to 864: 1 × 864, 2 × 432, 3 × 288, 4 × 216, 6 × 144, 8 × 108, 9 × 96, 12 × 72, 16 × 54, 18 × 48, 24 × 36, 27 × 32.

What is the sum of the factors of 864?

Adding all the factors of 864 together gives 2520. Excluding 864 itself, the proper factors sum to 1656.

Is 864 a perfect square?

No, 864 is not a perfect square. There is no whole number that multiplies by itself to give 864. The nearest perfect squares are 841 and 900.

What is the largest factor of 864 other than itself?

The largest factor of 864 apart from 864 itself is 432, since 864 ÷ 432 = 2.

How many factors does 864 have?

864 has 24 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864. You can verify this from the prime factorization 2⁵ × 3³: add 1 to each exponent and multiply, giving 6 × 4 = 24.

Explore more

Try another number in the factor calculator, break 864 down further with the prime factorization calculator, or compare 864 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.