Factor Calculator

Factors of 216

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216. In total, 216 has 16 factors. Its prime factorization is 2³ × 3³, and the sum of all its factors is 600.

All factors of 216

Here are all 16 factors of 216, listed from smallest to largest.

123468912182427365472108216

Factor pairs of 216

These 8 pairs of whole numbers each multiply to give 216.

1 × 216 = 216
2 × 108 = 216
3 × 72 = 216
4 × 54 = 216
6 × 36 = 216
8 × 27 = 216
9 × 24 = 216
12 × 18 = 216

Prime factorization of 216

Dividing 216 by the smallest prime at each step gives its prime factorization:

216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 216 = 2 × 2 × 2 × 3 × 3 × 3 = 2³ × 3³

The distinct prime factors of 216 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 216

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

Factor tree of 21621621082542273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 216

Number of factors16
Sum of factors600
Sum of proper factors384
Prime factorization2³ × 3³
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?Yes (6³)
ClassificationAbundant

What makes 216 interesting

  • 216 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.
  • 216 is a perfect cube: 6 × 6 × 6 = 216.
  • 216 is an abundant number: its proper factors sum to 384, which is 168 more than 216 itself.

How to find the factors of 216 yourself

Divide 216 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 √216 ≈ 14.70, because every factor above that pairs with one below it.

216 ÷ 1 = 216 ✓
216 ÷ 2 = 108 ✓
216 ÷ 3 = 72 ✓
216 ÷ 4 = 54 ✓
216 ÷ 6 = 36 ✓
216 ÷ 8 = 27 ✓
216 ÷ 9 = 24 ✓
216 ÷ 12 = 18 ✓

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

Numbers mathematically connected to 216.

Frequently asked questions about 216

What are the factors of 216?

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

Is 216 a prime number?

No, 216 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 216 is also divisible by 2.

What is the prime factorization of 216?

The prime factorization of 216 is 2³ × 3³. Written out in full: 2 × 2 × 2 × 3 × 3 × 3 = 216. Its distinct prime factors are 2, 3.

What two numbers multiply to give 216?

There are 8 pairs of whole numbers that multiply to 216: 1 × 216, 2 × 108, 3 × 72, 4 × 54, 6 × 36, 8 × 27, 9 × 24, 12 × 18.

What is the sum of the factors of 216?

Adding all the factors of 216 together gives 600. Excluding 216 itself, the proper factors sum to 384.

Is 216 a perfect square?

No, 216 is not a perfect square. There is no whole number that multiplies by itself to give 216. The nearest perfect squares are 196 and 225.

What is the largest factor of 216 other than itself?

The largest factor of 216 apart from 216 itself is 108, since 216 ÷ 108 = 2.

How many factors does 216 have?

216 has 16 factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216. You can verify this from the prime factorization 2³ × 3³: add 1 to each exponent and multiply, giving 4 × 4 = 16.

Explore more

Try another number in the factor calculator, break 216 down further with the prime factorization calculator, or compare 216 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.