Factor Calculator

Factors of 90

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. In total, 90 has 12 factors. Its prime factorization is 2 × 3² × 5, and the sum of all its factors is 234.

All factors of 90

Here are all 12 factors of 90, listed from smallest to largest.

123569101518304590

Factor pairs of 90

These 6 pairs of whole numbers each multiply to give 90.

1 × 90 = 90
2 × 45 = 90
3 × 30 = 90
5 × 18 = 90
6 × 15 = 90
9 × 10 = 90

Prime factorization of 90

Dividing 90 by the smallest prime at each step gives its prime factorization:

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

The distinct prime factors of 90 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 90

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

Factor tree of 909024531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 90

Number of factors12
Sum of factors234
Sum of proper factors144
Prime factorization2 × 3² × 5
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 90 interesting

  • 90 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.
  • 90 is an abundant number: its proper factors sum to 144, which is 54 more than 90 itself.
  • 90 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 90 yourself

Divide 90 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 √90 ≈ 9.49, because every factor above that pairs with one below it.

90 ÷ 1 = 90 ✓
90 ÷ 2 = 45 ✓
90 ÷ 3 = 30 ✓
90 ÷ 5 = 18 ✓
90 ÷ 6 = 15 ✓
90 ÷ 9 = 10 ✓

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

Numbers mathematically connected to 90.

Frequently asked questions about 90

What are the factors of 90?

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

Is 90 a prime number?

No, 90 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 90 is also divisible by 2.

What is the prime factorization of 90?

The prime factorization of 90 is 2 × 3² × 5. Written out in full: 2 × 3 × 3 × 5 = 90. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 90?

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

What is the sum of the factors of 90?

Adding all the factors of 90 together gives 234. Excluding 90 itself, the proper factors sum to 144.

Is 90 a perfect square?

No, 90 is not a perfect square. There is no whole number that multiplies by itself to give 90. The nearest perfect squares are 81 and 100.

What is the largest factor of 90 other than itself?

The largest factor of 90 apart from 90 itself is 45, since 90 ÷ 45 = 2.

How many factors does 90 have?

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

Explore more

Try another number in the factor calculator, break 90 down further with the prime factorization calculator, or compare 90 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.