Factors of 16
16 has 5 factors: 1, 2, 4, 8 and 16. This page shows the pairs that multiply to make 16, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 5 factors of 16
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5 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 × 16, 2 × 8 and 4 × 4
- Prime factorization
- 16 = 2⁴
Why these are the factors of 16
Two numbers form a factor pair of 16 when 16 squares can be arranged into a rectangle with those side lengths and none left over. 16 makes 3 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 16
Split 16 into any two factors, then keep splitting until only primes are left. The bottom row gives 16 = 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.
16 = 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 16
Most factors of 16 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: 16 ÷ 2 = 8 |
| 3 | The digits add up to a multiple of 3. Here they add to 7. | No: 16 ÷ 3 leaves remainder 1 |
| 4 | The last two digits form a multiple of 4. Here they are 16. | Yes: 16 ÷ 4 = 4 |
| 5 | The last digit is 0 or 5. Here it is 6. | No: 16 ÷ 5 leaves remainder 1 |
| 6 | It passes both the 2 rule and the 3 rule. | No: 16 ÷ 6 leaves remainder 4 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -11. | No: 16 ÷ 7 leaves remainder 2 |
| 8 | The last three digits form a multiple of 8. Here they are 16. | Yes: 16 ÷ 8 = 2 |
| 9 | The digits add up to a multiple of 9. Here they add to 7. | No: 16 ÷ 9 leaves remainder 7 |
| 10 | The last digit is 0. Here it is 6. | No: 16 ÷ 10 leaves remainder 6 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 5. | No: 16 ÷ 11 leaves remainder 5 |
Multiples of 16
Multiples run in the other direction: they are the numbers 16 divides into exactly. The list starts 16, 32, 48, 64, 80, 96 and goes on forever, growing by 16 each step. Every multiple of 16 has 16 in its own factor list.
The square root of 16
16 is a perfect square: 4 × 4 = 16, so its square root is exactly 4. That is also why one of its factor pairs forms a true square.
Everything else about 16
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 5, which matches the rule from 2⁴: add one to each exponent and multiply. |
| Factors added together | 31 |
| Compared with its own factors | Deficient: the factors below 16 add up to 15, which is less than 16 |
| Numbers below it sharing no factor | 8 of the numbers from 1 to 16 share no factor with 16 |
| 16 squared | 256 |
| 16 cubed | 4096 |
| A perfect square? | Yes: 4 × 4 |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 13 below, 17 above |
| In binary | 10000 |
| In hexadecimal | 10 |
| As a Roman numeral | XVI |
Find the factors of 16 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 16 exactly counts, including 1 and 16 itself.
Frequently asked questions
- What are the factors of 16?
- 16 has 5 factors: 1, 2, 4, 8, 16. Each one divides 16 exactly, with no remainder.
- Is 16 a prime number?
- No, 16 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 5 factors in total.
- What is the prime factorization of 16?
- 16 = 2 × 2 × 2 × 2, which is 2⁴ in exponent form. Whichever pair you split 16 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 16?
- There are 3: 1 × 16, 2 × 8 and 4 × 4. Each pair is a rectangle of 16 squares, with those two numbers as its sides.
- What is the square root of 16?
- √16 = 4 exactly, because 4 × 4 = 16. 16 is a perfect square.
- How many factors does 16 have?
- 5. You can read this off the prime factorization 2⁴ without listing anything: add one to each exponent and multiply the results.
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