Factor Calculator

Factors of 180

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. In total, 180 has 18 factors. Its prime factorization is 2² × 3² × 5, and the sum of all its factors is 546.

All factors of 180

Here are all 18 factors of 180, listed from smallest to largest.

123456910121518203036456090180

Factor pairs of 180

These 9 pairs of whole numbers each multiply to give 180.

1 × 180 = 180
2 × 90 = 180
3 × 60 = 180
4 × 45 = 180
5 × 36 = 180
6 × 30 = 180
9 × 20 = 180
10 × 18 = 180
12 × 15 = 180

Prime factorization of 180

Dividing 180 by the smallest prime at each step gives its prime factorization:

180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5

The distinct prime factors of 180 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 180

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

Factor tree of 18018029024531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 180

Number of factors18
Sum of factors546
Sum of proper factors366
Prime factorization2² × 3² × 5
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 180 interesting

  • 180 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.
  • 180 is an abundant number: its proper factors sum to 366, which is 186 more than 180 itself.
  • 180 is a highly composite number — it has more factors (18) than any smaller positive integer. Numbers like this are useful in measurement systems because they divide evenly so many ways.
  • 180 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 180 yourself

Divide 180 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 √180 ≈ 13.42, because every factor above that pairs with one below it.

180 ÷ 1 = 180 ✓
180 ÷ 2 = 90 ✓
180 ÷ 3 = 60 ✓
180 ÷ 4 = 45 ✓
180 ÷ 5 = 36 ✓
180 ÷ 6 = 30 ✓
180 ÷ 9 = 20 ✓
180 ÷ 10 = 18 ✓
180 ÷ 12 = 15 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. The factor calculator does this automatically for any number.

Numbers mathematically connected to 180.

Frequently asked questions about 180

What are the factors of 180?

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. That is 18 factors in total, counting both 1 and 180.

Is 180 a prime number?

No, 180 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 180 is also divisible by 2.

What is the prime factorization of 180?

The prime factorization of 180 is 2² × 3² × 5. Written out in full: 2 × 2 × 3 × 3 × 5 = 180. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 180?

There are 9 pairs of whole numbers that multiply to 180: 1 × 180, 2 × 90, 3 × 60, 4 × 45, 5 × 36, 6 × 30, 9 × 20, 10 × 18, 12 × 15.

What is the sum of the factors of 180?

Adding all the factors of 180 together gives 546. Excluding 180 itself, the proper factors sum to 366.

Is 180 a perfect square?

No, 180 is not a perfect square. There is no whole number that multiplies by itself to give 180. The nearest perfect squares are 169 and 196.

What is the largest factor of 180 other than itself?

The largest factor of 180 apart from 180 itself is 90, since 180 ÷ 90 = 2.

How many factors does 180 have?

180 has 18 factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. You can verify this from the prime factorization 2² × 3² × 5: add 1 to each exponent and multiply, giving 3 × 3 × 2 = 18.

Explore more

Try another number in the factor calculator, break 180 down further with the prime factorization calculator, or compare 180 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.