The number 31680
31680 is a composite number with 84 divisors. Its prime factorisation is × × 5 × 11. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 31680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31680: a Harshad number: divisible by its digit sum 18.
- 2
31680 is composite. Its prime factorisation is
- 3
The divisors add up to 118872; without 31680 itself that is 87192, so 31680 is abundant (87192 is more than 31680). Euler's totient φ(31680) = 7680 numbers up to 31680 share no factor with it.
- 4
The digits of 31680 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 103 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31680 = 2^{6} \times 3^{2} \times 5 \times 11 \]31680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 118872 |
| Euler totient φ(n) | 7680 |
| Square | 1003622400 |
| Cube | 31794757632000 |
| Square root | 177.988764 (= 24√55) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 103 |
| Scientific notation | 3.168 × |
31680 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand six hundred and eighty |
| Binary (base 2) | 111101111000000 |
| Octal (base 8) | 75700 |
| Hexadecimal (base 16) | 7BC0 |
| Base 3 | 1121110100 |
| As time | 31680 seconds = 8 h 48 min 0 s |
Is 31680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31680 ÷ 2 = 15840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31680 ÷ 3 = 10560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31680 ÷ 4 = 7920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31680 ÷ 5 = 6336) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31680 ÷ 6 = 5280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (31680 ÷ 8 = 3960) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31680 ÷ 9 = 3520) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31680 ÷ 10 = 3168) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (31680 ÷ 11 = 2880) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31680 ÷ 12 = 2640) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31680 a prime number?
No. 31680 = × × 5 × 11, so it is divisible by 2.
What are the factors of 31680?
1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 32, 33, 36, 40, 44, 45, 48, 55, 60, 64, 66, 72, 80, 88, 90, 96, 99, 110, 120, 132, 144, 160, 165, 176, 180, 192, 198, 220, 240, 264, 288, 320, 330, 352, 360, 396, 440, 480, 495, 528, 576, 660, 704, 720, 792, 880, 960, 990, 1056, 1320, 1440, 1584, 1760, 1980, 2112, 2640, 2880, 3168, 3520, 3960, 5280, 6336, 7920, 10560, 15840, 31680.
What is 31680 in binary?
111101111000000 (hexadecimal 7BC0, octal 75700).
What is the square root of 31680?
About 177.9888, exactly 24√55.
Is 31680 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 31680?
31680 is a Harshad number: divisible by its digit sum 18.