Factor Calculator

Factors of 108

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. In total, 108 has 12 factors. Its prime factorization is 2² × 3³, and the sum of all its factors is 280.

All factors of 108

Here are all 12 factors of 108, listed from smallest to largest.

1234691218273654108

Factor pairs of 108

These 6 pairs of whole numbers each multiply to give 108.

1 × 108 = 108
2 × 54 = 108
3 × 36 = 108
4 × 27 = 108
6 × 18 = 108
9 × 12 = 108

Prime factorization of 108

Dividing 108 by the smallest prime at each step gives its prime factorization:

108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

The distinct prime factors of 108 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 108

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

Factor tree of 1081082542273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 108

Number of factors12
Sum of factors280
Sum of proper factors172
Prime factorization2² × 3³
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 108 interesting

  • 108 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 108 is an abundant number: its proper factors sum to 172, which is 64 more than 108 itself.

How to find the factors of 108 yourself

Divide 108 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 √108 ≈ 10.39, because every factor above that pairs with one below it.

108 ÷ 1 = 108 ✓
108 ÷ 2 = 54 ✓
108 ÷ 3 = 36 ✓
108 ÷ 4 = 27 ✓
108 ÷ 6 = 18 ✓
108 ÷ 9 = 12 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. The factor calculator does this automatically for any number.

Numbers mathematically connected to 108.

Frequently asked questions about 108

What are the factors of 108?

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. That is 12 factors in total, counting both 1 and 108.

Is 108 a prime number?

No, 108 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 108 is also divisible by 2.

What is the prime factorization of 108?

The prime factorization of 108 is 2² × 3³. Written out in full: 2 × 2 × 3 × 3 × 3 = 108. Its distinct prime factors are 2, 3.

What two numbers multiply to give 108?

There are 6 pairs of whole numbers that multiply to 108: 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, 9 × 12.

What is the sum of the factors of 108?

Adding all the factors of 108 together gives 280. Excluding 108 itself, the proper factors sum to 172.

Is 108 a perfect square?

No, 108 is not a perfect square. There is no whole number that multiplies by itself to give 108. The nearest perfect squares are 100 and 121.

What is the largest factor of 108 other than itself?

The largest factor of 108 apart from 108 itself is 54, since 108 ÷ 54 = 2.

How many factors does 108 have?

108 has 12 factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. You can verify this from the prime factorization 2² × 3³: add 1 to each exponent and multiply, giving 3 × 4 = 12.

Explore more

Try another number in the factor calculator, break 108 down further with the prime factorization calculator, or compare 108 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.