The number 97992
97992 is a composite number with 24 divisors. Its prime factorisation is × × 1361. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 1361, 2722, 4083, 5444 … 97992.
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How to work it out
- 1
What is special about 97992: a Harshad number: divisible by its digit sum 36.
- 2
97992 is composite. Its prime factorisation is
- 3
The divisors add up to 265590; without 97992 itself that is 167598, so 97992 is abundant (167598 is more than 97992). Euler's totient φ(97992) = 32640 numbers up to 97992 share no factor with it.
- 4
The digits of 97992 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97992 = 2^{3} \times 3^{2} \times 1361 \]97992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 265590 |
| Euler totient φ(n) | 32640 |
| Square | 9602432064 |
| Cube | 940961522815488 |
| Square root | 313.036739 (= 6√2722) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.7992 × |
97992 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand nine hundred and ninety-two |
| Binary (base 2) | 10111111011001000 |
| Octal (base 8) | 277310 |
| Hexadecimal (base 16) | 17EC8 |
| Base 3 | 11222102100 |
| As time | 97992 seconds = 27 h 13 min 12 s |
Is 97992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97992 ÷ 2 = 48996) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97992 ÷ 3 = 32664) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97992 ÷ 4 = 24498) | 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 (97992 ÷ 6 = 16332) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (97992 ÷ 8 = 12249) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97992 ÷ 9 = 10888) | 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 (97992 ÷ 12 = 8166) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97992 a prime number?
No. 97992 = × × 1361, so it is divisible by 2.
What are the factors of 97992?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 1361, 2722, 4083, 5444, 8166, 10888, 12249, 16332, 24498, 32664, 48996, 97992.
What is 97992 in binary?
10111111011001000 (hexadecimal 17EC8, octal 277310).
What is the square root of 97992?
About 313.0367, exactly 6√2722.
Is 97992 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 97992?
97992 is a Harshad number: divisible by its digit sum 36.