The number 992
992 is a composite number with 12 divisors. Its prime factorisation is × 31. Divisors (12): 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
992 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
992 is composite. Its prime factorisation is
- 3
The divisors add up to 2016; without 992 itself that is 1024, so 992 is abundant (1024 is more than 992). Euler's totient φ(992) = 480 numbers up to 992 share no factor with it.
- 4
The digits of 992 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 992 = 2^{5} \times 31 \]992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2016 |
| Euler totient φ(n) | 480 |
| Square | 984064 |
| Cube | 976191488 |
| Square root | 31.496031 (= 4√62) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 111 |
| Scientific notation | 9.92 × |
992 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety-two |
| Roman numerals | CMXCII |
| Binary (base 2) | 1111100000 |
| Octal (base 8) | 1740 |
| Hexadecimal (base 16) | 3E0 |
| Base 3 | 1100202 |
| As time | 992 seconds = 16 min 32 s |
Is 992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (992 ÷ 2 = 496) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (992 ÷ 4 = 248) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (992 ÷ 8 = 124) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 992 a prime number?
No. 992 = × 31, so it is divisible by 2.
What are the factors of 992?
1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992.
What is 992 in binary?
1111100000 (hexadecimal 3E0, octal 1740).
What is the square root of 992?
About 31.4960, exactly 4√62.
What is 992 in Roman numerals?
CMXCII.
Is 992 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 992?
It is a composite number with 12 divisors.