Factor Calculator

Factors of 450

The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. In total, 450 has 18 factors. Its prime factorization is 2 × 3² × 5², and the sum of all its factors is 1209.

All factors of 450

Here are all 18 factors of 450, listed from smallest to largest.

123569101518253045507590150225450

Factor pairs of 450

These 9 pairs of whole numbers each multiply to give 450.

1 × 450 = 450
2 × 225 = 450
3 × 150 = 450
5 × 90 = 450
6 × 75 = 450
9 × 50 = 450
10 × 45 = 450
15 × 30 = 450
18 × 25 = 450

Prime factorization of 450

Dividing 450 by the smallest prime at each step gives its prime factorization:

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

The distinct prime factors of 450 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 450

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

Factor tree of 450450222537532555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 450

Number of factors18
Sum of factors1209
Sum of proper factors759
Prime factorization2 × 3² × 5²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 450 interesting

  • 450 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.
  • 450 is an abundant number: its proper factors sum to 759, which is 309 more than 450 itself.
  • 450 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 450 yourself

Divide 450 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 √450 ≈ 21.21, because every factor above that pairs with one below it.

450 ÷ 1 = 450 ✓
450 ÷ 2 = 225 ✓
450 ÷ 3 = 150 ✓
450 ÷ 5 = 90 ✓
450 ÷ 6 = 75 ✓
450 ÷ 9 = 50 ✓
450 ÷ 10 = 45 ✓
450 ÷ 15 = 30 ✓
450 ÷ 18 = 25 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. The factor calculator does this automatically for any number.

Numbers mathematically connected to 450.

Frequently asked questions about 450

What are the factors of 450?

The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. That is 18 factors in total, counting both 1 and 450.

Is 450 a prime number?

No, 450 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 450 is also divisible by 2.

What is the prime factorization of 450?

The prime factorization of 450 is 2 × 3² × 5². Written out in full: 2 × 3 × 3 × 5 × 5 = 450. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 450?

There are 9 pairs of whole numbers that multiply to 450: 1 × 450, 2 × 225, 3 × 150, 5 × 90, 6 × 75, 9 × 50, 10 × 45, 15 × 30, 18 × 25.

What is the sum of the factors of 450?

Adding all the factors of 450 together gives 1209. Excluding 450 itself, the proper factors sum to 759.

Is 450 a perfect square?

No, 450 is not a perfect square. There is no whole number that multiplies by itself to give 450. The nearest perfect squares are 441 and 484.

What is the largest factor of 450 other than itself?

The largest factor of 450 apart from 450 itself is 225, since 450 ÷ 225 = 2.

How many factors does 450 have?

450 has 18 factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450. You can verify this from the prime factorization 2 × 3² × 5²: add 1 to each exponent and multiply, giving 2 × 3 × 3 = 18.

Explore more

Try another number in the factor calculator, break 450 down further with the prime factorization calculator, or compare 450 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.