Factors of 100
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. No, 100 is a composite number. Its prime factorization is 2^2 × 5^2.
Factor pairs of 100
Every factor has a partner that multiplies with it to give 100. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle (here at 10 × 10), you have them all.
| Pair | Check |
|---|---|
| 1 and 100 | 1 × 100 = 100 |
| 2 and 50 | 2 × 50 = 100 |
| 4 and 25 | 4 × 25 = 100 |
| 5 and 20 | 5 × 20 = 100 |
| 10 and 10 | 10 × 10 = 100 |
Prime factorization of 100, step by step
Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.
| Step | Divide | Result |
|---|---|---|
| 1 | 100 ÷ 2 | 50 |
| 2 | 50 ÷ 2 | 25 |
| 3 | 25 ÷ 5 | 5 |
| 4 | 5 ÷ 5 | 1 |
So 100 = 2 × 2 × 5 × 5, written compactly as 2^2 × 5^2.
Divisibility checks for 100
The quick rules a student uses before dividing, applied to 100:
| Divisible by | Rule | For 100 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 0 | yes |
| 3 | digit sum divisible by 3 | digits add to 1 | no |
| 4 | last two digits divisible by 4 | 00 ÷ 4 | yes |
| 5 | last digit is 0 or 5 | last digit 0 | yes |
| 6 | divisible by both 2 and 3 | even, digit sum 1 | no |
| 8 | last three digits divisible by 8 | 100 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 1 | no |
| 10 | last digit is 0 | last digit 0 | yes |
Frequently Asked Questions
What are the factors of 100?
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Is 100 a prime number?
No, 100 is a composite number. Its prime factorization is 2^2 × 5^2.
How many factors does 100 have?
100 has 9 factors. You can get that count from the prime factorization without listing them: add 1 to each exponent in 2^2 × 5^2 and multiply -- (2+1) × (2+1) = 9.
Is 100 even or odd, and is it a perfect square?
100 is even (2 is one of its factors), and it is a perfect square: 10 × 10 = 100, which is why its factor list has an odd number of entries.
What is the sum of the factors of 100?
1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217. Leaving out 100 itself, the proper factors add to 117, more than 100, so 100 is an abundant number.
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