The number 31944
31944 is a composite number with 32 divisors. Its prime factorisation is × 3 × . Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 121, 132 … 31944.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
31944 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31944 is composite. Its prime factorisation is
- 3
The divisors add up to 87840; without 31944 itself that is 55896, so 31944 is abundant (55896 is more than 31944). Euler's totient φ(31944) = 9680 numbers up to 31944 share no factor with it.
- 4
The digits of 31944 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
\[ 31944 = 2^{3} \times 3 \times 11^{3} \]31944 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 87840 |
| Euler totient φ(n) | 9680 |
| Square | 1020419136 |
| Cube | 32596268880384 |
| Square root | 178.728845 (= 22√66) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1944 × |
31944 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and forty-four |
| Binary (base 2) | 111110011001000 |
| Octal (base 8) | 76310 |
| Hexadecimal (base 16) | 7CC8 |
| Base 3 | 1121211010 |
| As time | 31944 seconds = 8 h 52 min 24 s |
Is 31944 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31944 ÷ 2 = 15972) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31944 ÷ 3 = 10648) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31944 ÷ 4 = 7986) | 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 (31944 ÷ 6 = 5324) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (31944 ÷ 8 = 3993) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (31944 ÷ 11 = 2904) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31944 ÷ 12 = 2662) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31944 a prime number?
No. 31944 = × 3 × , so it is divisible by 2.
What are the factors of 31944?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 121, 132, 242, 264, 363, 484, 726, 968, 1331, 1452, 2662, 2904, 3993, 5324, 7986, 10648, 15972, 31944.
What is 31944 in binary?
111110011001000 (hexadecimal 7CC8, octal 76310).
What is the square root of 31944?
About 178.7288, exactly 22√66.
Is 31944 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 31944?
It is a composite number with 32 divisors.