The number 97920
97920 is a composite number with 96 divisors. Its prime factorisation is × × 5 × 17. Divisors (96): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24 … 97920.
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How to work it out
- 1
97920 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
97920 is composite. Its prime factorisation is
- 3
The divisors add up to 358020; without 97920 itself that is 260100, so 97920 is abundant (260100 is more than 97920). Euler's totient φ(97920) = 24576 numbers up to 97920 share no factor with it.
- 4
The digits of 97920 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 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97920 = 2^{7} \times 3^{2} \times 5 \times 17 \]97920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 358020 |
| Euler totient φ(n) | 24576 |
| Square | 9588326400 |
| Cube | 938888921088000 |
| Square root | 312.921715 (= 24√170) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 53 |
| Scientific notation | 9.792 × |
97920 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand nine hundred and twenty |
| Binary (base 2) | 10111111010000000 |
| Octal (base 8) | 277200 |
| Hexadecimal (base 16) | 17E80 |
| Base 3 | 11222022200 |
| As time | 97920 seconds = 27 h 12 min 0 s |
Is 97920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97920 ÷ 2 = 48960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97920 ÷ 3 = 32640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97920 ÷ 4 = 24480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (97920 ÷ 5 = 19584) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97920 ÷ 6 = 16320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (97920 ÷ 8 = 12240) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97920 ÷ 9 = 10880) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (97920 ÷ 10 = 9792) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97920 ÷ 12 = 8160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97920 a prime number?
No. 97920 = × × 5 × 17, so it is divisible by 2.
What are the factors of 97920?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 32, 34, 36, 40, 45, 48, 51, 60, 64, 68, 72, 80, 85, 90, 96, 102, 120, 128, 136, 144, 153, 160, 170, 180, 192, 204, 240, 255, 272, 288, 306, 320, 340, 360, 384, 408, 480, 510, 544, 576, 612, 640, 680, 720, 765, 816, 960, 1020, 1088, 1152, 1224, 1360, 1440, 1530, 1632, 1920, 2040, 2176, 2448, 2720, 2880, 3060, 3264, 4080, 4896, 5440, 5760, 6120, 6528, 8160, 9792, 10880, 12240, 16320, 19584, 24480, 32640, 48960, 97920.
What is 97920 in binary?
10111111010000000 (hexadecimal 17E80, octal 277200).
What is the square root of 97920?
About 312.9217, exactly 24√170.
Is 97920 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 97920?
It is a composite number with 96 divisors.