Factor Calculator · Practical guide
Factors of 100: Full List, Count, and Sum
100 has nine factors: 1, 2, 4, 5, 10, 20, 25, 50, and 100 — and they add up to 217.
At a glance
All the Factors of 100
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100 — every whole number that divides 100 with no remainder. That is 9 factors in total, and their sum is 217. Because 100 has more than two factors, it is a composite number, not a prime.
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Result
Factor Pairs of 100
Factors always come in pairs that multiply to the number itself. Working up from 1, the pairs stop when you reach the square root of 100, which is exactly 10:
| Factor Pair | Check |
|---|---|
| 1 and 100 | 1 x 100 = 100 |
| 2 and 50 | 2 x 50 = 100 |
| 4 and 25 | 4 x 25 = 100 |
| 5 and 20 | 5 x 20 = 100 |
| 10 and 10 | 10 x 10 = 100 |
The 10 x 10 pair is what makes 100 a perfect square — perfect squares always have an odd factor count because one factor pairs with itself.
Why There Are Exactly Nine
The prime factorization of 100 is 2^2 x 5^2. The factor-count shortcut multiplies each exponent plus one: (2+1) x (2+1) = 3 x 3 = 9. This works for any number — factor it into primes, add 1 to each exponent, and multiply.
Checking Your Work
Enter 100 above and the calculator returns the full sorted list, the count of 9, the sum of 217, and confirms that 100 is not prime — the same figures shown here, instantly, for any positive integer up to one trillion.
Frequently Asked Questions
Is 100 a prime number?
No. A prime has exactly two factors — 1 and itself. Since 100 is divisible by 2, 4, 5, 10, 20, 25, and 50 as well, it is composite.
What are the prime factors of 100?
Only 2 and 5. The complete prime factorization is 2 x 2 x 5 x 5, written as 2^2 x 5^2.
What is the greatest factor of 100 besides itself?
50. The largest proper factor of any even number is half of it, since 2 is its smallest factor greater than 1.
How is 100 different from a perfect number?
A perfect number equals the sum of its proper factors. The proper factors of 100 (1, 2, 4, 5, 10, 20, 25, 50) sum to 117, not 100, so 100 is abundant rather than perfect.