Factors of 120
120 has 16 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120. This page shows the pairs that multiply to make 120, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 16 factors of 120
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16 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 × 120, 2 × 60, 3 × 40, 4 × 30, 5 × 24, 6 × 20, 8 × 15 and 10 × 12
- Prime factorization
- 120 = 2³ × 3 × 5
Why these are the factors of 120
Two numbers form a factor pair of 120 when 120 squares can be arranged into a rectangle with those side lengths and none left over. 120 makes 8 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 120
Split 120 into any two factors, then keep splitting until only primes are left. The bottom row gives 120 = 2 × 2 × 2 × 3 × 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.
120 = 2 × 2 × 2 × 3 × 5
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 120
Most factors of 120 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: 120 ÷ 2 = 60 |
| 3 | The digits add up to a multiple of 3. Here they add to 3. | Yes: 120 ÷ 3 = 40 |
| 4 | The last two digits form a multiple of 4. Here they are 20. | Yes: 120 ÷ 4 = 30 |
| 5 | The last digit is 0 or 5. Here it is 0. | Yes: 120 ÷ 5 = 24 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 120 ÷ 6 = 20 |
| 7 | Double the last digit and subtract it from the rest. Here that gives 12. | No: 120 ÷ 7 leaves remainder 1 |
| 8 | The last three digits form a multiple of 8. Here they are 120. | Yes: 120 ÷ 8 = 15 |
| 9 | The digits add up to a multiple of 9. Here they add to 3. | No: 120 ÷ 9 leaves remainder 3 |
| 10 | The last digit is 0. Here it is 0. | Yes: 120 ÷ 10 = 12 |
| 11 | Add and subtract the digits alternately from the right. Here that gives -1. | No: 120 ÷ 11 leaves remainder 10 |
Multiples of 120
Multiples run in the other direction: they are the numbers 120 divides into exactly. The list starts 120, 240, 360, 480, 600, 720 and goes on forever, growing by 120 each step. Every multiple of 120 has 120 in its own factor list.
The square root of 120
√120 is not a whole number, because 120 sits between the perfect squares 100 and 121. Its exact simplified form is 2√30: the square factor moves out from under the root sign. The decimal 10.954451 is a rounded approximation, not the exact value.
Everything else about 120
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 16, which matches the rule from 2³ × 3 × 5: add one to each exponent and multiply. |
| Factors added together | 360 |
| Compared with its own factors | Abundant: the factors below 120 add up to 240, which is more than 120 |
| Numbers below it sharing no factor | 32 of the numbers from 1 to 120 share no factor with 120 |
| 120 squared | 14400 |
| 120 cubed | 1728000 |
| A perfect square? | No |
| A perfect cube? | No |
| A triangular number? | Yes |
| Nearest primes | 113 below, 127 above |
| In binary | 1111000 |
| In hexadecimal | 78 |
| As a Roman numeral | CXX |
Find the factors of 120 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 120 exactly counts, including 1 and 120 itself.
Frequently asked questions
- What are the factors of 120?
- 120 has 16 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each one divides 120 exactly, with no remainder.
- Is 120 a prime number?
- No, 120 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 16 factors in total.
- What is the prime factorization of 120?
- 120 = 2 × 2 × 2 × 3 × 5, which is 2³ × 3 × 5 in exponent form. Whichever pair you split 120 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 120?
- There are 8: 1 × 120, 2 × 60, 3 × 40, 4 × 30, 5 × 24, 6 × 20, 8 × 15 and 10 × 12. Each pair is a rectangle of 120 squares, with those two numbers as its sides.
- What is the square root of 120?
- √120 is irrational. Its exact simplified form is 2√30; as a decimal it is about 10.954451, which is a rounding rather than the exact value. 120 lies between the perfect squares 100 and 121.
- How many factors does 120 have?
- 16. You can read this off the prime factorization 2³ × 3 × 5 without listing anything: add one to each exponent and multiply the results.
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