The number 31644
31644 is a composite number with 24 divisors. Its prime factorisation is × × 293. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 293, 586, 879, 1172 … 31644.
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How to work it out
- 1
What is special about 31644: a Harshad number: divisible by its digit sum 18.
- 2
31644 is composite. Its prime factorisation is
- 3
The divisors add up to 82320; without 31644 itself that is 50676, so 31644 is abundant (50676 is more than 31644). Euler's totient φ(31644) = 10512 numbers up to 31644 share no factor with it.
- 4
The digits of 31644 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 77 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31644 = 2^{2} \times 3^{3} \times 293 \]31644 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 82320 |
| Euler totient φ(n) | 10512 |
| Square | 1001342736 |
| Cube | 31686489537984 |
| Square root | 177.887605 (= 6√879) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 77 |
| Scientific notation | 3.1644 × |
31644 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand six hundred and forty-four |
| Binary (base 2) | 111101110011100 |
| Octal (base 8) | 75634 |
| Hexadecimal (base 16) | 7B9C |
| Base 3 | 1121102000 |
| As time | 31644 seconds = 8 h 47 min 24 s |
Is 31644 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31644 ÷ 2 = 15822) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31644 ÷ 3 = 10548) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31644 ÷ 4 = 7911) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31644 ÷ 6 = 5274) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31644 ÷ 9 = 3516) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31644 ÷ 12 = 2637) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31644 a prime number?
No. 31644 = × × 293, so it is divisible by 2.
What are the factors of 31644?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 293, 586, 879, 1172, 1758, 2637, 3516, 5274, 7911, 10548, 15822, 31644.
What is 31644 in binary?
111101110011100 (hexadecimal 7B9C, octal 75634).
What is the square root of 31644?
About 177.8876, exactly 6√879.
Is 31644 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 31644?
31644 is a Harshad number: divisible by its digit sum 18.