Factors of 60
60 has 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. This page shows the pairs that multiply to make 60, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 12 factors of 60
123456101215203060
12 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 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10
- Prime factorization
- 60 = 2² × 3 × 5
Why these are the factors of 60
Two numbers form a factor pair of 60 when 60 squares can be arranged into a rectangle with those side lengths and none left over. 60 makes 6 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 60
Split 60 into any two factors, then keep splitting until only primes are left. The bottom row gives 60 = 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.
60 = 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 60
Most factors of 60 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: 60 ÷ 2 = 30 |
| 3 | The digits add up to a multiple of 3. Here they add to 6. | Yes: 60 ÷ 3 = 20 |
| 4 | The last two digits form a multiple of 4. Here they are 60. | Yes: 60 ÷ 4 = 15 |
| 5 | The last digit is 0 or 5. Here it is 0. | Yes: 60 ÷ 5 = 12 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 60 ÷ 6 = 10 |
| 7 | Double the last digit and subtract it from the rest. Here that gives 6. | No: 60 ÷ 7 leaves remainder 4 |
| 8 | The last three digits form a multiple of 8. Here they are 60. | No: 60 ÷ 8 leaves remainder 4 |
| 9 | The digits add up to a multiple of 9. Here they add to 6. | No: 60 ÷ 9 leaves remainder 6 |
| 10 | The last digit is 0. Here it is 0. | Yes: 60 ÷ 10 = 6 |
| 11 | Add and subtract the digits alternately from the right. Here that gives -6. | No: 60 ÷ 11 leaves remainder 5 |
Multiples of 60
Multiples run in the other direction: they are the numbers 60 divides into exactly. The list starts 60, 120, 180, 240, 300, 360 and goes on forever, growing by 60 each step. Every multiple of 60 has 60 in its own factor list.
The square root of 60
√60 is not a whole number, because 60 sits between the perfect squares 49 and 64. Its exact simplified form is 2√15: the square factor moves out from under the root sign. The decimal 7.745967 is a rounded approximation, not the exact value.
Everything else about 60
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 12, which matches the rule from 2² × 3 × 5: add one to each exponent and multiply. |
| Factors added together | 168 |
| Compared with its own factors | Abundant: the factors below 60 add up to 108, which is more than 60 |
| Numbers below it sharing no factor | 16 of the numbers from 1 to 60 share no factor with 60 |
| 60 squared | 3600 |
| 60 cubed | 216000 |
| A perfect square? | No |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 59 below, 61 above |
| In binary | 111100 |
| In hexadecimal | 3C |
| As a Roman numeral | LX |
Find the factors of 60 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 60 exactly counts, including 1 and 60 itself.
Frequently asked questions
- What are the factors of 60?
- 60 has 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Each one divides 60 exactly, with no remainder.
- Is 60 a prime number?
- No, 60 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 12 factors in total.
- What is the prime factorization of 60?
- 60 = 2 × 2 × 3 × 5, which is 2² × 3 × 5 in exponent form. Whichever pair you split 60 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 60?
- There are 6: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10. Each pair is a rectangle of 60 squares, with those two numbers as its sides.
- What is the square root of 60?
- √60 is irrational. Its exact simplified form is 2√15; as a decimal it is about 7.745967, which is a rounding rather than the exact value. 60 lies between the perfect squares 49 and 64.
- How many factors does 60 have?
- 12. You can read this off the prime factorization 2² × 3 × 5 without listing anything: add one to each exponent and multiply the results.
Related numbers
