Factor Calculator

Factors of 100

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. In total, 100 has 9 factors. Its prime factorization is 2² × 5², and the sum of all its factors is 217. 100 is also a perfect square, equal to 10 × 10.

All factors of 100

Here are all 9 factors of 100, listed from smallest to largest.

124510202550100

Factor pairs of 100

These 5 pairs of whole numbers each multiply to give 100.

1 × 100 = 100
2 × 50 = 100
4 × 25 = 100
5 × 20 = 100
10 × 10 = 100

Notice the pair (10, 10) — because 100 is a perfect square, this pair uses the same number twice.

Prime factorization of 100

Dividing 100 by the smallest prime at each step gives its prime factorization:

100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Result: 100 = 2 × 2 × 5 × 5 = 2² × 5²

The distinct prime factors of 100 are 2, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 100

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

Factor tree of 10010025022555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 100

Number of factors9
Sum of factors217
Sum of proper factors117
Prime factorization2² × 5²
Prime or composite?Composite
Even or odd?Even
Perfect square?Yes (10²)
Perfect cube?No
ClassificationAbundant

What makes 100 interesting

  • 100 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.
  • 100 is a perfect square: 10 × 10 = 100. This is why it has an odd number of factors (9) — the pair (10, 10) counts only once.
  • 100 is an abundant number: its proper factors sum to 117, which is 17 more than 100 itself.

How to find the factors of 100 yourself

Divide 100 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 √100 ≈ 10.00, because every factor above that pairs with one below it.

100 ÷ 1 = 100 ✓
100 ÷ 2 = 50 ✓
100 ÷ 4 = 25 ✓
100 ÷ 5 = 20 ✓
100 ÷ 10 = 10 ✓

Reading both columns gives every factor: 1, 2, 4, 5, 10, 20, 25, 50, 100. The factor calculator does this automatically for any number.

Numbers mathematically connected to 100.

Frequently asked questions about 100

What are the factors of 100?

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. That is 9 factors in total, counting both 1 and 100.

Is 100 a prime number?

No, 100 is not prime — it is a composite number with 9 factors. A prime number has exactly two factors, but 100 is also divisible by 2.

What is the prime factorization of 100?

The prime factorization of 100 is 2² × 5². Written out in full: 2 × 2 × 5 × 5 = 100. Its distinct prime factors are 2, 5.

What two numbers multiply to give 100?

There are 5 pairs of whole numbers that multiply to 100: 1 × 100, 2 × 50, 4 × 25, 5 × 20, 10 × 10.

What is the sum of the factors of 100?

Adding all the factors of 100 together gives 217. Excluding 100 itself, the proper factors sum to 117.

Is 100 a perfect square?

Yes, 100 is a perfect square. It equals 10 × 10. Perfect squares always have an odd number of factors — 100 has 9.

What is the largest factor of 100 other than itself?

The largest factor of 100 apart from 100 itself is 50, since 100 ÷ 50 = 2.

How many factors does 100 have?

100 has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50, and 100. You can verify this from the prime factorization 2² × 5²: add 1 to each exponent and multiply, giving 3 × 3 = 9.

Explore more

Try another number in the factor calculator, break 100 down further with the prime factorization calculator, or compare 100 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.