Factor Calculator

Factors of 75

The factors of 75 are 1, 3, 5, 15, 25, and 75. In total, 75 has 6 factors. Its prime factorization is 3 × 5², and the sum of all its factors is 124.

All factors of 75

Here are all 6 factors of 75, listed from smallest to largest.

135152575

Factor pairs of 75

These 3 pairs of whole numbers each multiply to give 75.

1 × 75 = 75
3 × 25 = 75
5 × 15 = 75

Prime factorization of 75

Dividing 75 by the smallest prime at each step gives its prime factorization:

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

The distinct prime factors of 75 are 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 75

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

Factor tree of 757532555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 75

Number of factors6
Sum of factors124
Sum of proper factors49
Prime factorization3 × 5²
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 75 interesting

  • 75 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.
  • 75 is a deficient number: its proper factors sum to 49, which is 26 less than 75 itself.

How to find the factors of 75 yourself

Divide 75 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 √75 ≈ 8.66, because every factor above that pairs with one below it.

75 ÷ 1 = 75 ✓
75 ÷ 3 = 25 ✓
75 ÷ 5 = 15 ✓

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

Numbers mathematically connected to 75.

Frequently asked questions about 75

What are the factors of 75?

The factors of 75 are 1, 3, 5, 15, 25, and 75. That is 6 factors in total, counting both 1 and 75.

Is 75 a prime number?

No, 75 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 75 is also divisible by 3.

What is the prime factorization of 75?

The prime factorization of 75 is 3 × 5². Written out in full: 3 × 5 × 5 = 75. Its distinct prime factors are 3, 5.

What two numbers multiply to give 75?

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

What is the sum of the factors of 75?

Adding all the factors of 75 together gives 124. Excluding 75 itself, the proper factors sum to 49.

Is 75 a perfect square?

No, 75 is not a perfect square. There is no whole number that multiplies by itself to give 75. The nearest perfect squares are 64 and 81.

What is the largest factor of 75 other than itself?

The largest factor of 75 apart from 75 itself is 25, since 75 ÷ 25 = 3.

How many factors does 75 have?

75 has 6 factors: 1, 3, 5, 15, 25, and 75. You can verify this from the prime factorization 3 × 5²: add 1 to each exponent and multiply, giving 2 × 3 = 6.

Explore more

Try another number in the factor calculator, break 75 down further with the prime factorization calculator, or compare 75 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.