Factors of 144
144 has 15 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144. This page shows the pairs that multiply to make 144, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 15 factors of 144
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15 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 × 144, 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16 and 12 × 12
- Prime factorization
- 144 = 2⁴ × 3²
Why these are the factors of 144
Two numbers form a factor pair of 144 when 144 squares can be arranged into a rectangle with those side lengths and none left over. 144 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 144
Split 144 into any two factors, then keep splitting until only primes are left. The bottom row gives 144 = 2 × 2 × 2 × 2 × 3 × 3. 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.
144 = 2 × 2 × 2 × 2 × 3 × 3
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 144
Most factors of 144 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 4. | Yes: 144 ÷ 2 = 72 |
| 3 | The digits add up to a multiple of 3. Here they add to 9. | Yes: 144 ÷ 3 = 48 |
| 4 | The last two digits form a multiple of 4. Here they are 44. | Yes: 144 ÷ 4 = 36 |
| 5 | The last digit is 0 or 5. Here it is 4. | No: 144 ÷ 5 leaves remainder 4 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 144 ÷ 6 = 24 |
| 7 | Double the last digit and subtract it from the rest. Here that gives 6. | No: 144 ÷ 7 leaves remainder 4 |
| 8 | The last three digits form a multiple of 8. Here they are 144. | Yes: 144 ÷ 8 = 18 |
| 9 | The digits add up to a multiple of 9. Here they add to 9. | Yes: 144 ÷ 9 = 16 |
| 10 | The last digit is 0. Here it is 4. | No: 144 ÷ 10 leaves remainder 4 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 1. | No: 144 ÷ 11 leaves remainder 1 |
Multiples of 144
Multiples run in the other direction: they are the numbers 144 divides into exactly. The list starts 144, 288, 432, 576, 720, 864 and goes on forever, growing by 144 each step. Every multiple of 144 has 144 in its own factor list.
The square root of 144
144 is a perfect square: 12 × 12 = 144, so its square root is exactly 12. That is also why one of its factor pairs forms a true square.
Everything else about 144
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 15, which matches the rule from 2⁴ × 3²: add one to each exponent and multiply. |
| Factors added together | 403 |
| Compared with its own factors | Abundant: the factors below 144 add up to 259, which is more than 144 |
| Numbers below it sharing no factor | 48 of the numbers from 1 to 144 share no factor with 144 |
| 144 squared | 20736 |
| 144 cubed | 2985984 |
| A perfect square? | Yes: 12 × 12 |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 139 below, 149 above |
| In binary | 10010000 |
| In hexadecimal | 90 |
| As a Roman numeral | CXLIV |
Find the factors of 144 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 144 exactly counts, including 1 and 144 itself.
Frequently asked questions
- What are the factors of 144?
- 144 has 15 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Each one divides 144 exactly, with no remainder.
- Is 144 a prime number?
- No, 144 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 15 factors in total.
- What is the prime factorization of 144?
- 144 = 2 × 2 × 2 × 2 × 3 × 3, which is 2⁴ × 3² in exponent form. Whichever pair you split 144 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 144?
- There are 8: 1 × 144, 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16 and 12 × 12. Each pair is a rectangle of 144 squares, with those two numbers as its sides.
- What is the square root of 144?
- √144 = 12 exactly, because 12 × 12 = 144. 144 is a perfect square.
- How many factors does 144 have?
- 15. You can read this off the prime factorization 2⁴ × 3² without listing anything: add one to each exponent and multiply the results.
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