Factor Calculator

Factors of 135

The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135. In total, 135 has 8 factors. Its prime factorization is 3³ × 5, and the sum of all its factors is 240.

All factors of 135

Here are all 8 factors of 135, listed from smallest to largest.

1359152745135

Factor pairs of 135

These 4 pairs of whole numbers each multiply to give 135.

1 × 135 = 135
3 × 45 = 135
5 × 27 = 135
9 × 15 = 135

Prime factorization of 135

Dividing 135 by the smallest prime at each step gives its prime factorization:

135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 135 = 3 × 3 × 3 × 5 = 3³ × 5

The distinct prime factors of 135 are 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 135

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

Factor tree of 13513534531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 135

Number of factors8
Sum of factors240
Sum of proper factors105
Prime factorization3³ × 5
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 135 interesting

  • 135 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 135 is a deficient number: its proper factors sum to 105, which is 30 less than 135 itself.

How to find the factors of 135 yourself

Divide 135 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 √135 ≈ 11.62, because every factor above that pairs with one below it.

135 ÷ 1 = 135 ✓
135 ÷ 3 = 45 ✓
135 ÷ 5 = 27 ✓
135 ÷ 9 = 15 ✓

Reading both columns gives every factor: 1, 3, 5, 9, 15, 27, 45, 135. The factor calculator does this automatically for any number.

Numbers mathematically connected to 135.

Frequently asked questions about 135

What are the factors of 135?

The factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135. That is 8 factors in total, counting both 1 and 135.

Is 135 a prime number?

No, 135 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 135 is also divisible by 3.

What is the prime factorization of 135?

The prime factorization of 135 is 3³ × 5. Written out in full: 3 × 3 × 3 × 5 = 135. Its distinct prime factors are 3, 5.

What two numbers multiply to give 135?

There are 4 pairs of whole numbers that multiply to 135: 1 × 135, 3 × 45, 5 × 27, 9 × 15.

What is the sum of the factors of 135?

Adding all the factors of 135 together gives 240. Excluding 135 itself, the proper factors sum to 105.

Is 135 a perfect square?

No, 135 is not a perfect square. There is no whole number that multiplies by itself to give 135. The nearest perfect squares are 121 and 144.

What is the largest factor of 135 other than itself?

The largest factor of 135 apart from 135 itself is 45, since 135 ÷ 45 = 3.

How many factors does 135 have?

135 has 8 factors: 1, 3, 5, 9, 15, 27, 45, and 135. You can verify this from the prime factorization 3³ × 5: add 1 to each exponent and multiply, giving 4 × 2 = 8.

Explore more

Try another number in the factor calculator, break 135 down further with the prime factorization calculator, or compare 135 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.