Factor Calculator

Factors of 960

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960. In total, 960 has 28 factors. Its prime factorization is 2⁶ × 3 × 5, and the sum of all its factors is 3048.

All factors of 960

Here are all 28 factors of 960, listed from smallest to largest.

12345681012151620243032404860648096120160192240320480960

Factor pairs of 960

These 14 pairs of whole numbers each multiply to give 960.

1 × 960 = 960
2 × 480 = 960
3 × 320 = 960
4 × 240 = 960
5 × 192 = 960
6 × 160 = 960
8 × 120 = 960
10 × 96 = 960
12 × 80 = 960
15 × 64 = 960
16 × 60 = 960
20 × 48 = 960
24 × 40 = 960
30 × 32 = 960

Prime factorization of 960

Dividing 960 by the smallest prime at each step gives its prime factorization:

960 ÷ 2 = 480
480 ÷ 2 = 240
240 ÷ 2 = 120
120 ÷ 2 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 = 2⁶ × 3 × 5

The distinct prime factors of 960 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 960

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

Factor tree of 96096024802240212026023021535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 960

Number of factors28
Sum of factors3048
Sum of proper factors2088
Prime factorization2⁶ × 3 × 5
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 960 interesting

  • 960 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 14 different ways.
  • 960 is an abundant number: its proper factors sum to 2088, which is 1128 more than 960 itself.
  • 960 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 960 yourself

Divide 960 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 √960 ≈ 30.98, because every factor above that pairs with one below it.

960 ÷ 1 = 960 ✓
960 ÷ 2 = 480 ✓
960 ÷ 3 = 320 ✓
960 ÷ 4 = 240 ✓
960 ÷ 5 = 192 ✓
960 ÷ 6 = 160 ✓
960 ÷ 8 = 120 ✓
960 ÷ 10 = 96 ✓
960 ÷ 12 = 80 ✓
960 ÷ 15 = 64 ✓
960 ÷ 16 = 60 ✓
960 ÷ 20 = 48 ✓
960 ÷ 24 = 40 ✓
960 ÷ 30 = 32 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960. The factor calculator does this automatically for any number.

Numbers mathematically connected to 960.

Frequently asked questions about 960

What are the factors of 960?

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960. That is 28 factors in total, counting both 1 and 960.

Is 960 a prime number?

No, 960 is not prime — it is a composite number with 28 factors. A prime number has exactly two factors, but 960 is also divisible by 2.

What is the prime factorization of 960?

The prime factorization of 960 is 2⁶ × 3 × 5. Written out in full: 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 = 960. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 960?

There are 14 pairs of whole numbers that multiply to 960: 1 × 960, 2 × 480, 3 × 320, 4 × 240, 5 × 192, 6 × 160, 8 × 120, 10 × 96, 12 × 80, 15 × 64, 16 × 60, 20 × 48, 24 × 40, 30 × 32.

What is the sum of the factors of 960?

Adding all the factors of 960 together gives 3048. Excluding 960 itself, the proper factors sum to 2088.

Is 960 a perfect square?

No, 960 is not a perfect square. There is no whole number that multiplies by itself to give 960. The nearest perfect squares are 900 and 961.

What is the largest factor of 960 other than itself?

The largest factor of 960 apart from 960 itself is 480, since 960 ÷ 480 = 2.

How many factors does 960 have?

960 has 28 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 960. You can verify this from the prime factorization 2⁶ × 3 × 5: add 1 to each exponent and multiply, giving 7 × 2 × 2 = 28.

Explore more

Try another number in the factor calculator, break 960 down further with the prime factorization calculator, or compare 960 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.