Factors of 64
64 has 7 factors: 1, 2, 4, 8, 16, 32 and 64. This page shows the pairs that multiply to make 64, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 7 factors of 64
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7 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 × 64, 2 × 32, 4 × 16 and 8 × 8
- Prime factorization
- 64 = 2⁶
Why these are the factors of 64
Two numbers form a factor pair of 64 when 64 squares can be arranged into a rectangle with those side lengths and none left over. 64 makes 4 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 64
Split 64 into any two factors, then keep splitting until only primes are left. The bottom row gives 64 = 2 × 2 × 2 × 2 × 2 × 2. 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.
64 = 2 × 2 × 2 × 2 × 2 × 2
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 64
Most factors of 64 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: 64 ÷ 2 = 32 |
| 3 | The digits add up to a multiple of 3. Here they add to 10. | No: 64 ÷ 3 leaves remainder 1 |
| 4 | The last two digits form a multiple of 4. Here they are 64. | Yes: 64 ÷ 4 = 16 |
| 5 | The last digit is 0 or 5. Here it is 4. | No: 64 ÷ 5 leaves remainder 4 |
| 6 | It passes both the 2 rule and the 3 rule. | No: 64 ÷ 6 leaves remainder 4 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -2. | No: 64 ÷ 7 leaves remainder 1 |
| 8 | The last three digits form a multiple of 8. Here they are 64. | Yes: 64 ÷ 8 = 8 |
| 9 | The digits add up to a multiple of 9. Here they add to 10. | No: 64 ÷ 9 leaves remainder 1 |
| 10 | The last digit is 0. Here it is 4. | No: 64 ÷ 10 leaves remainder 4 |
| 11 | Add and subtract the digits alternately from the right. Here that gives -2. | No: 64 ÷ 11 leaves remainder 9 |
Multiples of 64
Multiples run in the other direction: they are the numbers 64 divides into exactly. The list starts 64, 128, 192, 256, 320, 384 and goes on forever, growing by 64 each step. Every multiple of 64 has 64 in its own factor list.
The square root of 64
64 is a perfect square: 8 × 8 = 64, so its square root is exactly 8. That is also why one of its factor pairs forms a true square.
Everything else about 64
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 7, which matches the rule from 2⁶: add one to each exponent and multiply. |
| Factors added together | 127 |
| Compared with its own factors | Deficient: the factors below 64 add up to 63, which is less than 64 |
| Numbers below it sharing no factor | 32 of the numbers from 1 to 64 share no factor with 64 |
| 64 squared | 4096 |
| 64 cubed | 262144 |
| A perfect square? | Yes: 8 × 8 |
| A perfect cube? | Yes: 4 × 4 × 4 |
| A triangular number? | No |
| Nearest primes | 61 below, 67 above |
| In binary | 1000000 |
| In hexadecimal | 40 |
| As a Roman numeral | LXIV |
Find the factors of 64 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 64 exactly counts, including 1 and 64 itself.
Frequently asked questions
- What are the factors of 64?
- 64 has 7 factors: 1, 2, 4, 8, 16, 32, 64. Each one divides 64 exactly, with no remainder.
- Is 64 a prime number?
- No, 64 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 7 factors in total.
- What is the prime factorization of 64?
- 64 = 2 × 2 × 2 × 2 × 2 × 2, which is 2⁶ in exponent form. Whichever pair you split 64 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 64?
- There are 4: 1 × 64, 2 × 32, 4 × 16 and 8 × 8. Each pair is a rectangle of 64 squares, with those two numbers as its sides.
- What is the square root of 64?
- √64 = 8 exactly, because 8 × 8 = 64. 64 is a perfect square.
- How many factors does 64 have?
- 7. You can read this off the prime factorization 2⁶ without listing anything: add one to each exponent and multiply the results.
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