Factors of 100
100 has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50 and 100. This page shows the pairs that multiply to make 100, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 9 factors of 100
124510202550100
9 factors
Strictly, every factor also has a negative twin, because two negative numbers multiply to a positive one. School questions almost always mean the positive factors, which is what this page lists.
- Factor pairs
- 1 × 100, 2 × 50, 4 × 25, 5 × 20 and 10 × 10
- Prime factorization
- 100 = 2² × 5²
Why these are the factors of 100
Two numbers form a factor pair of 100 when 100 squares can be arranged into a rectangle with those side lengths and none left over. 100 makes 5 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 100
Split 100 into any two factors, then keep splitting until only primes are left. The bottom row gives 100 = 2 × 2 × 5 × 5. Try a different first split: the tree changes shape, but it always ends on the same primes. Click any circled number to split it another way.
100 = 2 × 2 × 5 × 5
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 100
Most factors of 100 can be found without dividing. Each rule below looks at one small part of the number, such as the last digit or the digit sum, and each row shows the exact value the rule checks, so you can verify it yourself.
| Rule | It looks at | Verdict |
|---|---|---|
| 2 | The last digit is even. Here it is 0. | Yes: 100 ÷ 2 = 50 |
| 3 | The digits add up to a multiple of 3. Here they add to 1. | No: 100 ÷ 3 leaves remainder 1 |
| 4 | The last two digits form a multiple of 4. Here they are 0. | Yes: 100 ÷ 4 = 25 |
| 5 | The last digit is 0 or 5. Here it is 0. | Yes: 100 ÷ 5 = 20 |
| 6 | It passes both the 2 rule and the 3 rule. | No: 100 ÷ 6 leaves remainder 4 |
| 7 | Double the last digit and subtract it from the rest. Here that gives 10. | No: 100 ÷ 7 leaves remainder 2 |
| 8 | The last three digits form a multiple of 8. Here they are 100. | No: 100 ÷ 8 leaves remainder 4 |
| 9 | The digits add up to a multiple of 9. Here they add to 1. | No: 100 ÷ 9 leaves remainder 1 |
| 10 | The last digit is 0. Here it is 0. | Yes: 100 ÷ 10 = 10 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 1. | No: 100 ÷ 11 leaves remainder 1 |
Multiples of 100
Multiples run in the other direction: they are the numbers 100 divides into exactly. The list starts 100, 200, 300, 400, 500, 600 and goes on forever, growing by 100 each step. Every multiple of 100 has 100 in its own factor list.
The square root of 100
100 is a perfect square: 10 × 10 = 100, so its square root is exactly 10. That is also why one of its factor pairs forms a true square.
Everything else about 100
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 9, which matches the rule from 2² × 5²: add one to each exponent and multiply. |
| Factors added together | 217 |
| Compared with its own factors | Abundant: the factors below 100 add up to 117, which is more than 100 |
| Numbers below it sharing no factor | 40 of the numbers from 1 to 100 share no factor with 100 |
| 100 squared | 10000 |
| 100 cubed | 1000000 |
| A perfect square? | Yes: 10 × 10 |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 97 below, 101 above |
| In binary | 1100100 |
| In hexadecimal | 64 |
| As a Roman numeral | C |
Find the factors of 100 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 100 exactly counts, including 1 and 100 itself.
Frequently asked questions
- What are the factors of 100?
- 100 has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50, 100. Each one divides 100 exactly, with no remainder.
- Is 100 a prime number?
- No, 100 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 9 factors in total.
- What is the prime factorization of 100?
- 100 = 2 × 2 × 5 × 5, which is 2² × 5² in exponent form. Whichever pair you split 100 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 100?
- There are 5: 1 × 100, 2 × 50, 4 × 25, 5 × 20 and 10 × 10. Each pair is a rectangle of 100 squares, with those two numbers as its sides.
- What is the square root of 100?
- √100 = 10 exactly, because 10 × 10 = 100. 100 is a perfect square.
- How many factors does 100 have?
- 9. You can read this off the prime factorization 2² × 5² without listing anything: add one to each exponent and multiply the results.
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