Factor Calculator

Factors of 360

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. In total, 360 has 24 factors. Its prime factorization is 2³ × 3² × 5, and the sum of all its factors is 1170.

All factors of 360

Here are all 24 factors of 360, listed from smallest to largest.

1234568910121518202430364045607290120180360

Factor pairs of 360

These 12 pairs of whole numbers each multiply to give 360.

1 × 360 = 360
2 × 180 = 360
3 × 120 = 360
4 × 90 = 360
5 × 72 = 360
6 × 60 = 360
8 × 45 = 360
9 × 40 = 360
10 × 36 = 360
12 × 30 = 360
15 × 24 = 360
18 × 20 = 360

Prime factorization of 360

Dividing 360 by the smallest prime at each step gives its prime factorization:

360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5

The distinct prime factors of 360 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 360

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

Factor tree of 360360218029024531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 360

Number of factors24
Sum of factors1170
Sum of proper factors810
Prime factorization2³ × 3² × 5
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 360 interesting

  • 360 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
  • 360 is an abundant number: its proper factors sum to 810, which is 450 more than 360 itself.
  • 360 is a highly composite number — it has more factors (24) than any smaller positive integer. Numbers like this are useful in measurement systems because they divide evenly so many ways.
  • 360 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 360 yourself

Divide 360 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 √360 ≈ 18.97, because every factor above that pairs with one below it.

360 ÷ 1 = 360 ✓
360 ÷ 2 = 180 ✓
360 ÷ 3 = 120 ✓
360 ÷ 4 = 90 ✓
360 ÷ 5 = 72 ✓
360 ÷ 6 = 60 ✓
360 ÷ 8 = 45 ✓
360 ÷ 9 = 40 ✓
360 ÷ 10 = 36 ✓
360 ÷ 12 = 30 ✓
360 ÷ 15 = 24 ✓
360 ÷ 18 = 20 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. The factor calculator does this automatically for any number.

Numbers mathematically connected to 360.

Frequently asked questions about 360

What are the factors of 360?

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. That is 24 factors in total, counting both 1 and 360.

Is 360 a prime number?

No, 360 is not prime — it is a composite number with 24 factors. A prime number has exactly two factors, but 360 is also divisible by 2.

What is the prime factorization of 360?

The prime factorization of 360 is 2³ × 3² × 5. Written out in full: 2 × 2 × 2 × 3 × 3 × 5 = 360. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 360?

There are 12 pairs of whole numbers that multiply to 360: 1 × 360, 2 × 180, 3 × 120, 4 × 90, 5 × 72, 6 × 60, 8 × 45, 9 × 40, 10 × 36, 12 × 30, 15 × 24, 18 × 20.

What is the sum of the factors of 360?

Adding all the factors of 360 together gives 1170. Excluding 360 itself, the proper factors sum to 810.

Is 360 a perfect square?

No, 360 is not a perfect square. There is no whole number that multiplies by itself to give 360. The nearest perfect squares are 324 and 361.

What is the largest factor of 360 other than itself?

The largest factor of 360 apart from 360 itself is 180, since 360 ÷ 180 = 2.

How many factors does 360 have?

360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. You can verify this from the prime factorization 2³ × 3² × 5: add 1 to each exponent and multiply, giving 4 × 3 × 2 = 24.

Explore more

Try another number in the factor calculator, break 360 down further with the prime factorization calculator, or compare 360 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.