Factor Calculator

Factors of 225

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225. In total, 225 has 9 factors. Its prime factorization is 3² × 5², and the sum of all its factors is 403. 225 is also a perfect square, equal to 15 × 15.

All factors of 225

Here are all 9 factors of 225, listed from smallest to largest.

135915254575225

Factor pairs of 225

These 5 pairs of whole numbers each multiply to give 225.

1 × 225 = 225
3 × 75 = 225
5 × 45 = 225
9 × 25 = 225
15 × 15 = 225

Notice the pair (15, 15) — because 225 is a perfect square, this pair uses the same number twice.

Prime factorization of 225

Dividing 225 by the smallest prime at each step gives its prime factorization:

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

The distinct prime factors of 225 are 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 225

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

Factor tree of 22522537532555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 225

Number of factors9
Sum of factors403
Sum of proper factors178
Prime factorization3² × 5²
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (15²)
Perfect cube?No
ClassificationDeficient

What makes 225 interesting

  • 225 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 225 is a perfect square: 15 × 15 = 225. This is why it has an odd number of factors (9) — the pair (15, 15) counts only once.
  • 225 is a deficient number: its proper factors sum to 178, which is 47 less than 225 itself.

How to find the factors of 225 yourself

Divide 225 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 √225 ≈ 15.00, because every factor above that pairs with one below it.

225 ÷ 1 = 225 ✓
225 ÷ 3 = 75 ✓
225 ÷ 5 = 45 ✓
225 ÷ 9 = 25 ✓
225 ÷ 15 = 15 ✓

Reading both columns gives every factor: 1, 3, 5, 9, 15, 25, 45, 75, 225. The factor calculator does this automatically for any number.

Numbers mathematically connected to 225.

Frequently asked questions about 225

What are the factors of 225?

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225. That is 9 factors in total, counting both 1 and 225.

Is 225 a prime number?

No, 225 is not prime — it is a composite number with 9 factors. A prime number has exactly two factors, but 225 is also divisible by 3.

What is the prime factorization of 225?

The prime factorization of 225 is 3² × 5². Written out in full: 3 × 3 × 5 × 5 = 225. Its distinct prime factors are 3, 5.

What two numbers multiply to give 225?

There are 5 pairs of whole numbers that multiply to 225: 1 × 225, 3 × 75, 5 × 45, 9 × 25, 15 × 15.

What is the sum of the factors of 225?

Adding all the factors of 225 together gives 403. Excluding 225 itself, the proper factors sum to 178.

Is 225 a perfect square?

Yes, 225 is a perfect square. It equals 15 × 15. Perfect squares always have an odd number of factors — 225 has 9.

What is the largest factor of 225 other than itself?

The largest factor of 225 apart from 225 itself is 75, since 225 ÷ 75 = 3.

How many factors does 225 have?

225 has 9 factors: 1, 3, 5, 9, 15, 25, 45, 75, and 225. You can verify this from the prime factorization 3² × 5²: add 1 to each exponent and multiply, giving 3 × 3 = 9.

Explore more

Try another number in the factor calculator, break 225 down further with the prime factorization calculator, or compare 225 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.