Factor Calculator

Factors of 45

The factors of 45 are 1, 3, 5, 9, 15, and 45. In total, 45 has 6 factors. Its prime factorization is 3² × 5, and the sum of all its factors is 78.

All factors of 45

Here are all 6 factors of 45, listed from smallest to largest.

13591545

Factor pairs of 45

These 3 pairs of whole numbers each multiply to give 45.

1 × 45 = 45
3 × 15 = 45
5 × 9 = 45

Prime factorization of 45

Dividing 45 by the smallest prime at each step gives its prime factorization:

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

The distinct prime factors of 45 are 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 45

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

Factor tree of 454531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 45

Number of factors6
Sum of factors78
Sum of proper factors33
Prime factorization3² × 5
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 45 interesting

  • 45 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 3 different ways.
  • 45 is a deficient number: its proper factors sum to 33, which is 12 less than 45 itself.
  • 45 is a triangular number — it is the sum of the first 9 whole numbers (1 + 2 + … + 9 = 45).

How to find the factors of 45 yourself

Divide 45 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 √45 ≈ 6.71, because every factor above that pairs with one below it.

45 ÷ 1 = 45 ✓
45 ÷ 3 = 15 ✓
45 ÷ 5 = 9 ✓

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

Numbers mathematically connected to 45.

Frequently asked questions about 45

What are the factors of 45?

The factors of 45 are 1, 3, 5, 9, 15, and 45. That is 6 factors in total, counting both 1 and 45.

Is 45 a prime number?

No, 45 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 45 is also divisible by 3.

What is the prime factorization of 45?

The prime factorization of 45 is 3² × 5. Written out in full: 3 × 3 × 5 = 45. Its distinct prime factors are 3, 5.

What two numbers multiply to give 45?

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

What is the sum of the factors of 45?

Adding all the factors of 45 together gives 78. Excluding 45 itself, the proper factors sum to 33.

Is 45 a perfect square?

No, 45 is not a perfect square. There is no whole number that multiplies by itself to give 45. The nearest perfect squares are 36 and 49.

What is the largest factor of 45 other than itself?

The largest factor of 45 apart from 45 itself is 15, since 45 ÷ 15 = 3.

How many factors does 45 have?

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

Explore more

Try another number in the factor calculator, break 45 down further with the prime factorization calculator, or compare 45 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.