The number 31920
31920 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7 × 19. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21 … 31920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31920: a Harshad number: divisible by its digit sum 15.
- 2
31920 is composite. Its prime factorisation is
- 3
The divisors add up to 119040; without 31920 itself that is 87120, so 31920 is abundant (87120 is more than 31920). Euler's totient φ(31920) = 6912 numbers up to 31920 share no factor with it.
- 4
The digits of 31920 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31920 = 2^{4} \times 3 \times 5 \times 7 \times 19 \]31920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 119040 |
| Euler totient φ(n) | 6912 |
| Square | 1018886400 |
| Cube | 32522853888000 |
| Square root | 178.661691 (= 4√1995) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.192 × |
31920 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and twenty |
| Binary (base 2) | 111110010110000 |
| Octal (base 8) | 76260 |
| Hexadecimal (base 16) | 7CB0 |
| Base 3 | 1121210020 |
| As time | 31920 seconds = 8 h 52 min 0 s |
Is 31920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31920 ÷ 2 = 15960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31920 ÷ 3 = 10640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31920 ÷ 4 = 7980) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31920 ÷ 5 = 6384) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31920 ÷ 6 = 5320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (31920 ÷ 7 = 4560) | 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 (31920 ÷ 8 = 3990) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31920 ÷ 10 = 3192) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31920 ÷ 12 = 2660) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31920 a prime number?
No. 31920 = × 3 × 5 × 7 × 19, so it is divisible by 2.
What are the factors of 31920?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920.
What is 31920 in binary?
111110010110000 (hexadecimal 7CB0, octal 76260).
What is the square root of 31920?
About 178.6617, exactly 4√1995.
Is 31920 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 31920?
31920 is a Harshad number: divisible by its digit sum 15.