The number 16320
16320 is a composite number with 56 divisors. Its prime factorisation is × 3 × 5 × 17. Divisors (56): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32 … 16320.
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How to work it out
- 1
What is special about 16320: a Harshad number: divisible by its digit sum 12.
- 2
16320 is composite. Its prime factorisation is
- 3
The divisors add up to 54864; without 16320 itself that is 38544, so 16320 is abundant (38544 is more than 16320). Euler's totient φ(16320) = 4096 numbers up to 16320 share no factor with it.
- 4
The digits of 16320 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16320 = 2^{6} \times 3 \times 5 \times 17 \]16320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 54864 |
| Euler totient φ(n) | 4096 |
| Square | 266342400 |
| Cube | 4346707968000 |
| Square root | 127.749755 (= 8√255) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 53 |
| Scientific notation | 1.632 × |
16320 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand three hundred and twenty |
| Binary (base 2) | 11111111000000 |
| Octal (base 8) | 37700 |
| Hexadecimal (base 16) | 3FC0 |
| Base 3 | 211101110 |
| As time | 16320 seconds = 4 h 32 min 0 s |
Is 16320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (16320 ÷ 2 = 8160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (16320 ÷ 3 = 5440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (16320 ÷ 4 = 4080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (16320 ÷ 5 = 3264) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (16320 ÷ 6 = 2720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (16320 ÷ 8 = 2040) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (16320 ÷ 10 = 1632) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (16320 ÷ 12 = 1360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16320 a prime number?
No. 16320 = × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 16320?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 136, 160, 170, 192, 204, 240, 255, 272, 320, 340, 408, 480, 510, 544, 680, 816, 960, 1020, 1088, 1360, 1632, 2040, 2720, 3264, 4080, 5440, 8160, 16320.
What is 16320 in binary?
11111111000000 (hexadecimal 3FC0, octal 37700).
What is the square root of 16320?
About 127.7498, exactly 8√255.
Is 16320 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 16320?
16320 is a Harshad number: divisible by its digit sum 12.