The number 31008
31008 is a composite number with 48 divisors. Its prime factorisation is × 3 × 17 × 19. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 16, 17, 19, 24, 32, 34, 38, 48, 51 … 31008.
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How to work it out
- 1
What is special about 31008: a Harshad number: divisible by its digit sum 12.
- 2
31008 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 31008 itself that is 59712, so 31008 is abundant (59712 is more than 31008). Euler's totient φ(31008) = 9216 numbers up to 31008 share no factor with it.
- 4
The digits of 31008 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31008 = 2^{5} \times 3 \times 17 \times 19 \]31008 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 9216 |
| Square | 961496064 |
| Cube | 29814069952512 |
| Square root | 176.090886 (= 4√1938) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1008 × |
31008 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand and eight |
| Binary (base 2) | 111100100100000 |
| Octal (base 8) | 74440 |
| Hexadecimal (base 16) | 7920 |
| Base 3 | 1120112110 |
| As time | 31008 seconds = 8 h 36 min 48 s |
Is 31008 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31008 ÷ 2 = 15504) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31008 ÷ 3 = 10336) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31008 ÷ 4 = 7752) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31008 ÷ 6 = 5168) | 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 (31008 ÷ 8 = 3876) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31008 ÷ 12 = 2584) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31008 a prime number?
No. 31008 = × 3 × 17 × 19, so it is divisible by 2.
What are the factors of 31008?
1, 2, 3, 4, 6, 8, 12, 16, 17, 19, 24, 32, 34, 38, 48, 51, 57, 68, 76, 96, 102, 114, 136, 152, 204, 228, 272, 304, 323, 408, 456, 544, 608, 646, 816, 912, 969, 1292, 1632, 1824, 1938, 2584, 3876, 5168, 7752, 10336, 15504, 31008.
What is 31008 in binary?
111100100100000 (hexadecimal 7920, octal 74440).
What is the square root of 31008?
About 176.0909, exactly 4√1938.
Is 31008 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31008?
31008 is a Harshad number: divisible by its digit sum 12.