Factors of 96
96 has 12 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. This page shows the pairs that multiply to make 96, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 12 factors of 96
123468121624324896
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 × 96, 2 × 48, 3 × 32, 4 × 24, 6 × 16 and 8 × 12
- Prime factorization
- 96 = 2⁵ × 3
Why these are the factors of 96
Two numbers form a factor pair of 96 when 96 squares can be arranged into a rectangle with those side lengths and none left over. 96 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 96
Split 96 into any two factors, then keep splitting until only primes are left. The bottom row gives 96 = 2 × 2 × 2 × 2 × 2 × 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.
96 = 2 × 2 × 2 × 2 × 2 × 3
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 96
Most factors of 96 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: 96 ÷ 2 = 48 |
| 3 | The digits add up to a multiple of 3. Here they add to 15. | Yes: 96 ÷ 3 = 32 |
| 4 | The last two digits form a multiple of 4. Here they are 96. | Yes: 96 ÷ 4 = 24 |
| 5 | The last digit is 0 or 5. Here it is 6. | No: 96 ÷ 5 leaves remainder 1 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 96 ÷ 6 = 16 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -3. | No: 96 ÷ 7 leaves remainder 5 |
| 8 | The last three digits form a multiple of 8. Here they are 96. | Yes: 96 ÷ 8 = 12 |
| 9 | The digits add up to a multiple of 9. Here they add to 15. | No: 96 ÷ 9 leaves remainder 6 |
| 10 | The last digit is 0. Here it is 6. | No: 96 ÷ 10 leaves remainder 6 |
| 11 | Add and subtract the digits alternately from the right. Here that gives -3. | No: 96 ÷ 11 leaves remainder 8 |
Multiples of 96
Multiples run in the other direction: they are the numbers 96 divides into exactly. The list starts 96, 192, 288, 384, 480, 576 and goes on forever, growing by 96 each step. Every multiple of 96 has 96 in its own factor list.
The square root of 96
√96 is not a whole number, because 96 sits between the perfect squares 81 and 100. Its exact simplified form is 4√6: the square factor moves out from under the root sign. The decimal 9.797959 is a rounded approximation, not the exact value.
Everything else about 96
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 12, which matches the rule from 2⁵ × 3: add one to each exponent and multiply. |
| Factors added together | 252 |
| Compared with its own factors | Abundant: the factors below 96 add up to 156, which is more than 96 |
| Numbers below it sharing no factor | 32 of the numbers from 1 to 96 share no factor with 96 |
| 96 squared | 9216 |
| 96 cubed | 884736 |
| A perfect square? | No |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 89 below, 97 above |
| In binary | 1100000 |
| In hexadecimal | 60 |
| As a Roman numeral | XCVI |
Find the factors of 96 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 96 exactly counts, including 1 and 96 itself.
Frequently asked questions
- What are the factors of 96?
- 96 has 12 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. Each one divides 96 exactly, with no remainder.
- Is 96 a prime number?
- No, 96 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 96?
- 96 = 2 × 2 × 2 × 2 × 2 × 3, which is 2⁵ × 3 in exponent form. Whichever pair you split 96 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 96?
- There are 6: 1 × 96, 2 × 48, 3 × 32, 4 × 24, 6 × 16 and 8 × 12. Each pair is a rectangle of 96 squares, with those two numbers as its sides.
- What is the square root of 96?
- √96 is irrational. Its exact simplified form is 4√6; as a decimal it is about 9.797959, which is a rounding rather than the exact value. 96 lies between the perfect squares 81 and 100.
- How many factors does 96 have?
- 12. You can read this off the prime factorization 2⁵ × 3 without listing anything: add one to each exponent and multiply the results.
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