Factors of 36
36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36. This page shows the pairs that multiply to make 36, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 9 factors of 36
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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 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6
- Prime factorization
- 36 = 2² × 3²
Why these are the factors of 36
Two numbers form a factor pair of 36 when 36 squares can be arranged into a rectangle with those side lengths and none left over. 36 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 36
Split 36 into any two factors, then keep splitting until only primes are left. The bottom row gives 36 = 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.
36 = 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 36
Most factors of 36 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 6. | Yes: 36 ÷ 2 = 18 |
| 3 | The digits add up to a multiple of 3. Here they add to 9. | Yes: 36 ÷ 3 = 12 |
| 4 | The last two digits form a multiple of 4. Here they are 36. | Yes: 36 ÷ 4 = 9 |
| 5 | The last digit is 0 or 5. Here it is 6. | No: 36 ÷ 5 leaves remainder 1 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 36 ÷ 6 = 6 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -9. | No: 36 ÷ 7 leaves remainder 1 |
| 8 | The last three digits form a multiple of 8. Here they are 36. | No: 36 ÷ 8 leaves remainder 4 |
| 9 | The digits add up to a multiple of 9. Here they add to 9. | Yes: 36 ÷ 9 = 4 |
| 10 | The last digit is 0. Here it is 6. | No: 36 ÷ 10 leaves remainder 6 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 3. | No: 36 ÷ 11 leaves remainder 3 |
Multiples of 36
Multiples run in the other direction: they are the numbers 36 divides into exactly. The list starts 36, 72, 108, 144, 180, 216 and goes on forever, growing by 36 each step. Every multiple of 36 has 36 in its own factor list.
The square root of 36
36 is a perfect square: 6 × 6 = 36, so its square root is exactly 6. That is also why one of its factor pairs forms a true square.
Everything else about 36
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 9, which matches the rule from 2² × 3²: add one to each exponent and multiply. |
| Factors added together | 91 |
| Compared with its own factors | Abundant: the factors below 36 add up to 55, which is more than 36 |
| Numbers below it sharing no factor | 12 of the numbers from 1 to 36 share no factor with 36 |
| 36 squared | 1296 |
| 36 cubed | 46656 |
| A perfect square? | Yes: 6 × 6 |
| A perfect cube? | No |
| A triangular number? | Yes |
| Nearest primes | 31 below, 37 above |
| In binary | 100100 |
| In hexadecimal | 24 |
| As a Roman numeral | XXXVI |
Find the factors of 36 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 36 exactly counts, including 1 and 36 itself.
Frequently asked questions
- What are the factors of 36?
- 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Each one divides 36 exactly, with no remainder.
- Is 36 a prime number?
- No, 36 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 36?
- 36 = 2 × 2 × 3 × 3, which is 2² × 3² in exponent form. Whichever pair you split 36 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 36?
- There are 5: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. Each pair is a rectangle of 36 squares, with those two numbers as its sides.
- What is the square root of 36?
- √36 = 6 exactly, because 6 × 6 = 36. 36 is a perfect square.
- How many factors does 36 have?
- 9. You can read this off the prime factorization 2² × 3² without listing anything: add one to each exponent and multiply the results.
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