Factor Calculator

Factors of 900

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900. In total, 900 has 27 factors. Its prime factorization is 2² × 3² × 5², and the sum of all its factors is 2821. 900 is also a perfect square, equal to 30 × 30.

All factors of 900

Here are all 27 factors of 900, listed from smallest to largest.

123456910121518202530364550607590100150180225300450900

Factor pairs of 900

These 14 pairs of whole numbers each multiply to give 900.

1 × 900 = 900
2 × 450 = 900
3 × 300 = 900
4 × 225 = 900
5 × 180 = 900
6 × 150 = 900
9 × 100 = 900
10 × 90 = 900
12 × 75 = 900
15 × 60 = 900
18 × 50 = 900
20 × 45 = 900
25 × 36 = 900
30 × 30 = 900

Notice the pair (30, 30) — because 900 is a perfect square, this pair uses the same number twice.

Prime factorization of 900

Dividing 900 by the smallest prime at each step gives its prime factorization:

900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Result: 900 = 2 × 2 × 3 × 3 × 5 × 5 = 2² × 3² × 5²

The distinct prime factors of 900 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 900

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

Factor tree of 9009002450222537532555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 900

Number of factors27
Sum of factors2821
Sum of proper factors1921
Prime factorization2² × 3² × 5²
Prime or composite?Composite
Even or odd?Even
Perfect square?Yes (30²)
Perfect cube?No
ClassificationAbundant

What makes 900 interesting

  • 900 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 14 different ways.
  • 900 is a perfect square: 30 × 30 = 900. This is why it has an odd number of factors (27) — the pair (30, 30) counts only once.
  • 900 is an abundant number: its proper factors sum to 1921, which is 1021 more than 900 itself.
  • 900 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 900 yourself

Divide 900 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 √900 ≈ 30.00, because every factor above that pairs with one below it.

900 ÷ 1 = 900 ✓
900 ÷ 2 = 450 ✓
900 ÷ 3 = 300 ✓
900 ÷ 4 = 225 ✓
900 ÷ 5 = 180 ✓
900 ÷ 6 = 150 ✓
900 ÷ 9 = 100 ✓
900 ÷ 10 = 90 ✓
900 ÷ 12 = 75 ✓
900 ÷ 15 = 60 ✓
900 ÷ 18 = 50 ✓
900 ÷ 20 = 45 ✓
900 ÷ 25 = 36 ✓
900 ÷ 30 = 30 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900. The factor calculator does this automatically for any number.

Numbers mathematically connected to 900.

Frequently asked questions about 900

What are the factors of 900?

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900. That is 27 factors in total, counting both 1 and 900.

Is 900 a prime number?

No, 900 is not prime — it is a composite number with 27 factors. A prime number has exactly two factors, but 900 is also divisible by 2.

What is the prime factorization of 900?

The prime factorization of 900 is 2² × 3² × 5². Written out in full: 2 × 2 × 3 × 3 × 5 × 5 = 900. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 900?

There are 14 pairs of whole numbers that multiply to 900: 1 × 900, 2 × 450, 3 × 300, 4 × 225, 5 × 180, 6 × 150, 9 × 100, 10 × 90, 12 × 75, 15 × 60, 18 × 50, 20 × 45, 25 × 36, 30 × 30.

What is the sum of the factors of 900?

Adding all the factors of 900 together gives 2821. Excluding 900 itself, the proper factors sum to 1921.

Is 900 a perfect square?

Yes, 900 is a perfect square. It equals 30 × 30. Perfect squares always have an odd number of factors — 900 has 27.

What is the largest factor of 900 other than itself?

The largest factor of 900 apart from 900 itself is 450, since 900 ÷ 450 = 2.

How many factors does 900 have?

900 has 27 factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900. You can verify this from the prime factorization 2² × 3² × 5²: add 1 to each exponent and multiply, giving 3 × 3 × 3 = 27.

Explore more

Try another number in the factor calculator, break 900 down further with the prime factorization calculator, or compare 900 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.