Factor Calculator

Factors of 768

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768. In total, 768 has 18 factors. Its prime factorization is 2⁸ × 3, and the sum of all its factors is 2044.

All factors of 768

Here are all 18 factors of 768, listed from smallest to largest.

12346812162432486496128192256384768

Factor pairs of 768

These 9 pairs of whole numbers each multiply to give 768.

1 × 768 = 768
2 × 384 = 768
3 × 256 = 768
4 × 192 = 768
6 × 128 = 768
8 × 96 = 768
12 × 64 = 768
16 × 48 = 768
24 × 32 = 768

Prime factorization of 768

Dividing 768 by the smallest prime at each step gives its prime factorization:

768 ÷ 2 = 384
384 ÷ 2 = 192
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
Result: 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2⁸ × 3

The distinct prime factors of 768 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 768

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

Factor tree of 768768238421922962482242122623
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 768

Number of factors18
Sum of factors2044
Sum of proper factors1276
Prime factorization2⁸ × 3
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 768 interesting

  • 768 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 9 different ways.
  • 768 is an abundant number: its proper factors sum to 1276, which is 508 more than 768 itself.

How to find the factors of 768 yourself

Divide 768 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 √768 ≈ 27.71, because every factor above that pairs with one below it.

768 ÷ 1 = 768 ✓
768 ÷ 2 = 384 ✓
768 ÷ 3 = 256 ✓
768 ÷ 4 = 192 ✓
768 ÷ 6 = 128 ✓
768 ÷ 8 = 96 ✓
768 ÷ 12 = 64 ✓
768 ÷ 16 = 48 ✓
768 ÷ 24 = 32 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. The factor calculator does this automatically for any number.

Numbers mathematically connected to 768.

Frequently asked questions about 768

What are the factors of 768?

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768. That is 18 factors in total, counting both 1 and 768.

Is 768 a prime number?

No, 768 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 768 is also divisible by 2.

What is the prime factorization of 768?

The prime factorization of 768 is 2⁸ × 3. Written out in full: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 768. Its distinct prime factors are 2, 3.

What two numbers multiply to give 768?

There are 9 pairs of whole numbers that multiply to 768: 1 × 768, 2 × 384, 3 × 256, 4 × 192, 6 × 128, 8 × 96, 12 × 64, 16 × 48, 24 × 32.

What is the sum of the factors of 768?

Adding all the factors of 768 together gives 2044. Excluding 768 itself, the proper factors sum to 1276.

Is 768 a perfect square?

No, 768 is not a perfect square. There is no whole number that multiplies by itself to give 768. The nearest perfect squares are 729 and 784.

What is the largest factor of 768 other than itself?

The largest factor of 768 apart from 768 itself is 384, since 768 ÷ 384 = 2.

How many factors does 768 have?

768 has 18 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768. You can verify this from the prime factorization 2⁸ × 3: add 1 to each exponent and multiply, giving 9 × 2 = 18.

Explore more

Try another number in the factor calculator, break 768 down further with the prime factorization calculator, or compare 768 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.