The number 7992
7992 is a composite number with 32 divisors. Its prime factorisation is × × 37. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 37, 54, 72, 74 … 7992.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7992: a Harshad number: divisible by its digit sum 27.
- 2
7992 is composite. Its prime factorisation is
- 3
The divisors add up to 22800; without 7992 itself that is 14808, so 7992 is abundant (14808 is more than 7992). Euler's totient φ(7992) = 2592 numbers up to 7992 share no factor with it.
- 4
The digits of 7992 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7992 = 2^{3} \times 3^{3} \times 37 \]7992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 22800 |
| Euler totient φ(n) | 2592 |
| Square | 63872064 |
| Cube | 510465535488 |
| Square root | 89.397987 (= 6√222) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.992 × |
7992 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and ninety-two |
| Binary (base 2) | 1111100111000 |
| Octal (base 8) | 17470 |
| Hexadecimal (base 16) | 1F38 |
| Base 3 | 101222000 |
| As time | 7992 seconds = 2 h 13 min 12 s |
Is 7992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7992 ÷ 2 = 3996) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7992 ÷ 3 = 2664) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7992 ÷ 4 = 1998) | 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 (7992 ÷ 6 = 1332) | 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 (7992 ÷ 8 = 999) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7992 ÷ 9 = 888) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7992 ÷ 12 = 666) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7992 a prime number?
No. 7992 = × × 37, so it is divisible by 2.
What are the factors of 7992?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 37, 54, 72, 74, 108, 111, 148, 216, 222, 296, 333, 444, 666, 888, 999, 1332, 1998, 2664, 3996, 7992.
What is 7992 in binary?
1111100111000 (hexadecimal 1F38, octal 17470).
What is the square root of 7992?
About 89.3980, exactly 6√222.
Is 7992 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 7992?
7992 is a Harshad number: divisible by its digit sum 27.