The number 31152
31152 is a composite number with 40 divisors. Its prime factorisation is × 3 × 11 × 59. Divisors (40): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 59, 66 … 31152.
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How to work it out
- 1
What is special about 31152: a Harshad number: divisible by its digit sum 12.
- 2
31152 is composite. Its prime factorisation is
- 3
The divisors add up to 89280; without 31152 itself that is 58128, so 31152 is abundant (58128 is more than 31152). Euler's totient φ(31152) = 9280 numbers up to 31152 share no factor with it.
- 4
The digits of 31152 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 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31152 = 2^{4} \times 3 \times 11 \times 59 \]31152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 89280 |
| Euler totient φ(n) | 9280 |
| Square | 970447104 |
| Cube | 30231368183808 |
| Square root | 176.499292 (= 4√1947) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.1152 × |
31152 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand one hundred and fifty-two |
| Binary (base 2) | 111100110110000 |
| Octal (base 8) | 74660 |
| Hexadecimal (base 16) | 79B0 |
| Base 3 | 1120201210 |
| As time | 31152 seconds = 8 h 39 min 12 s |
Is 31152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31152 ÷ 2 = 15576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31152 ÷ 3 = 10384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31152 ÷ 4 = 7788) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31152 ÷ 6 = 5192) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (31152 ÷ 8 = 3894) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (31152 ÷ 11 = 2832) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31152 ÷ 12 = 2596) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31152 a prime number?
No. 31152 = × 3 × 11 × 59, so it is divisible by 2.
What are the factors of 31152?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 59, 66, 88, 118, 132, 176, 177, 236, 264, 354, 472, 528, 649, 708, 944, 1298, 1416, 1947, 2596, 2832, 3894, 5192, 7788, 10384, 15576, 31152.
What is 31152 in binary?
111100110110000 (hexadecimal 79B0, octal 74660).
What is the square root of 31152?
About 176.4993, exactly 4√1947.
Is 31152 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31152?
31152 is a Harshad number: divisible by its digit sum 12.