The number 31992
31992 is a composite number with 32 divisors. Its prime factorisation is × 3 × 31 × 43. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 24, 31, 43, 62, 86, 93, 124, 129, 172 … 31992.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31992: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
31992 is composite. Its prime factorisation is
- 3
The divisors add up to 84480; without 31992 itself that is 52488, so 31992 is abundant (52488 is more than 31992). Euler's totient φ(31992) = 10080 numbers up to 31992 share no factor with it.
- 4
The digits of 31992 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 191 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31992 = 2^{3} \times 3 \times 31 \times 43 \]31992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 84480 |
| Euler totient φ(n) | 10080 |
| Square | 1023488064 |
| Cube | 32743430143488 |
| Square root | 178.863076 (= 2√7998) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 191 |
| Scientific notation | 3.1992 × |
31992 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and ninety-two |
| Binary (base 2) | 111110011111000 |
| Octal (base 8) | 76370 |
| Hexadecimal (base 16) | 7CF8 |
| Base 3 | 1121212220 |
| As time | 31992 seconds = 8 h 53 min 12 s |
Is 31992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31992 ÷ 2 = 15996) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31992 ÷ 3 = 10664) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31992 ÷ 4 = 7998) | 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 (31992 ÷ 6 = 5332) | 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 (31992 ÷ 8 = 3999) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31992 ÷ 12 = 2666) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31992 a prime number?
No. 31992 = × 3 × 31 × 43, so it is divisible by 2.
What are the factors of 31992?
1, 2, 3, 4, 6, 8, 12, 24, 31, 43, 62, 86, 93, 124, 129, 172, 186, 248, 258, 344, 372, 516, 744, 1032, 1333, 2666, 3999, 5332, 7998, 10664, 15996, 31992.
What is 31992 in binary?
111110011111000 (hexadecimal 7CF8, octal 76370).
What is the square root of 31992?
About 178.8631, exactly 2√7998.
Is 31992 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 31992?
31992 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.