The number 97760
97760 is a composite number with 48 divisors. Its prime factorisation is × 5 × 13 × 47. Divisors (48): 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 47, 52, 65, 80 … 97760.
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How to work it out
- 1
97760 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
97760 is composite. Its prime factorisation is
- 3
The divisors add up to 254016; without 97760 itself that is 156256, so 97760 is abundant (156256 is more than 97760). Euler's totient φ(97760) = 35328 numbers up to 97760 share no factor with it.
- 4
The digits of 97760 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 97 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97760 = 2^{5} \times 5 \times 13 \times 47 \]97760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 254016 |
| Euler totient φ(n) | 35328 |
| Square | 9557017600 |
| Cube | 934294040576000 |
| Square root | 312.665956 (= 4√6110) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 97 |
| Scientific notation | 9.776 × |
97760 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand seven hundred and sixty |
| Binary (base 2) | 10111110111100000 |
| Octal (base 8) | 276740 |
| Hexadecimal (base 16) | 17DE0 |
| Base 3 | 11222002202 |
| As time | 97760 seconds = 27 h 9 min 20 s |
Is 97760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97760 ÷ 2 = 48880) | 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 (97760 ÷ 4 = 24440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (97760 ÷ 5 = 19552) | 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 (97760 ÷ 8 = 12220) | 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 | Yes (97760 ÷ 10 = 9776) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 97760 a prime number?
No. 97760 = × 5 × 13 × 47, so it is divisible by 2.
What are the factors of 97760?
1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 47, 52, 65, 80, 94, 104, 130, 160, 188, 208, 235, 260, 376, 416, 470, 520, 611, 752, 940, 1040, 1222, 1504, 1880, 2080, 2444, 3055, 3760, 4888, 6110, 7520, 9776, 12220, 19552, 24440, 48880, 97760.
What is 97760 in binary?
10111110111100000 (hexadecimal 17DE0, octal 276740).
What is the square root of 97760?
About 312.6660, exactly 4√6110.
Is 97760 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 97760?
It is a composite number with 48 divisors.