The number 31296
31296 is a composite number with 28 divisors. Its prime factorisation is × 3 × 163. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 163, 192, 326 … 31296.
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How to work it out
- 1
31296 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31296 is composite. Its prime factorisation is
- 3
The divisors add up to 83312; without 31296 itself that is 52016, so 31296 is abundant (52016 is more than 31296). Euler's totient φ(31296) = 10368 numbers up to 31296 share no factor with it.
- 4
The digits of 31296 add up to 21, 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
\[ 31296 = 2^{6} \times 3 \times 163 \]31296 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 83312 |
| Euler totient φ(n) | 10368 |
| Square | 979439616 |
| Cube | 30652542222336 |
| Square root | 176.906755 (= 8√489) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1296 × |
31296 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand two hundred and ninety-six |
| Binary (base 2) | 111101001000000 |
| Octal (base 8) | 75100 |
| Hexadecimal (base 16) | 7A40 |
| Base 3 | 1120221010 |
| As time | 31296 seconds = 8 h 41 min 36 s |
Is 31296 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31296 ÷ 2 = 15648) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31296 ÷ 3 = 10432) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31296 ÷ 4 = 7824) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31296 ÷ 6 = 5216) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (31296 ÷ 8 = 3912) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31296 ÷ 12 = 2608) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31296 a prime number?
No. 31296 = × 3 × 163, so it is divisible by 2.
What are the factors of 31296?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 163, 192, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 5216, 7824, 10432, 15648, 31296.
What is 31296 in binary?
111101001000000 (hexadecimal 7A40, octal 75100).
What is the square root of 31296?
About 176.9068, exactly 8√489.
Is 31296 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 31296?
It is a composite number with 28 divisors.