Factor Calculator

Factors of 312

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312. In total, 312 has 16 factors. Its prime factorization is 2³ × 3 × 13, and the sum of all its factors is 840.

All factors of 312

Here are all 16 factors of 312, listed from smallest to largest.

12346812132426395278104156312

Factor pairs of 312

These 8 pairs of whole numbers each multiply to give 312.

1 × 312 = 312
2 × 156 = 312
3 × 104 = 312
4 × 78 = 312
6 × 52 = 312
8 × 39 = 312
12 × 26 = 312
13 × 24 = 312

Prime factorization of 312

Dividing 312 by the smallest prime at each step gives its prime factorization:

312 ÷ 2 = 156
156 ÷ 2 = 78
78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
Result: 312 = 2 × 2 × 2 × 3 × 13 = 2³ × 3 × 13

The distinct prime factors of 312 are 2, 3, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 312

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

Factor tree of 3123122156278239313
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 312

Number of factors16
Sum of factors840
Sum of proper factors528
Prime factorization2³ × 3 × 13
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 312 interesting

  • 312 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 312 is an abundant number: its proper factors sum to 528, which is 216 more than 312 itself.
  • 312 has 3 distinct prime factors (2, 3, 13), which is why it has so many divisors.

How to find the factors of 312 yourself

Divide 312 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 √312 ≈ 17.66, because every factor above that pairs with one below it.

312 ÷ 1 = 312 ✓
312 ÷ 2 = 156 ✓
312 ÷ 3 = 104 ✓
312 ÷ 4 = 78 ✓
312 ÷ 6 = 52 ✓
312 ÷ 8 = 39 ✓
312 ÷ 12 = 26 ✓
312 ÷ 13 = 24 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. The factor calculator does this automatically for any number.

Numbers mathematically connected to 312.

Frequently asked questions about 312

What are the factors of 312?

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312. That is 16 factors in total, counting both 1 and 312.

Is 312 a prime number?

No, 312 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 312 is also divisible by 2.

What is the prime factorization of 312?

The prime factorization of 312 is 2³ × 3 × 13. Written out in full: 2 × 2 × 2 × 3 × 13 = 312. Its distinct prime factors are 2, 3, 13.

What two numbers multiply to give 312?

There are 8 pairs of whole numbers that multiply to 312: 1 × 312, 2 × 156, 3 × 104, 4 × 78, 6 × 52, 8 × 39, 12 × 26, 13 × 24.

What is the sum of the factors of 312?

Adding all the factors of 312 together gives 840. Excluding 312 itself, the proper factors sum to 528.

Is 312 a perfect square?

No, 312 is not a perfect square. There is no whole number that multiplies by itself to give 312. The nearest perfect squares are 289 and 324.

What is the largest factor of 312 other than itself?

The largest factor of 312 apart from 312 itself is 156, since 312 ÷ 156 = 2.

How many factors does 312 have?

312 has 16 factors: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312. You can verify this from the prime factorization 2³ × 3 × 13: add 1 to each exponent and multiply, giving 4 × 2 × 2 = 16.

Explore more

Try another number in the factor calculator, break 312 down further with the prime factorization calculator, or compare 312 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.