The number 97680
97680 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 11 × 37. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 97680.
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How to work it out
- 1
What is special about 97680: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
- 2
97680 is composite. Its prime factorisation is
- 3
The divisors add up to 339264; without 97680 itself that is 241584, so 97680 is abundant (241584 is more than 97680). Euler's totient φ(97680) = 23040 numbers up to 97680 share no factor with it.
- 4
The digits of 97680 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97680 = 2^{4} \times 3 \times 5 \times 11 \times 37 \]97680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 339264 |
| Euler totient φ(n) | 23040 |
| Square | 9541382400 |
| Cube | 932002232832000 |
| Square root | 312.537998 (= 4√6105) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.768 × |
97680 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand six hundred and eighty |
| Binary (base 2) | 10111110110010000 |
| Octal (base 8) | 276620 |
| Hexadecimal (base 16) | 17D90 |
| Base 3 | 11221222210 |
| As time | 97680 seconds = 27 h 8 min 0 s |
Is 97680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97680 ÷ 2 = 48840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97680 ÷ 3 = 32560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97680 ÷ 4 = 24420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (97680 ÷ 5 = 19536) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97680 ÷ 6 = 16280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (97680 ÷ 8 = 12210) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (97680 ÷ 10 = 9768) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (97680 ÷ 11 = 8880) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97680 ÷ 12 = 8140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97680 a prime number?
No. 97680 = × 3 × 5 × 11 × 37, so it is divisible by 2.
What are the factors of 97680?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 37, 40, 44, 48, 55, 60, 66, 74, 80, 88, 110, 111, 120, 132, 148, 165, 176, 185, 220, 222, 240, 264, 296, 330, 370, 407, 440, 444, 528, 555, 592, 660, 740, 814, 880, 888, 1110, 1221, 1320, 1480, 1628, 1776, 2035, 2220, 2442, 2640, 2960, 3256, 4070, 4440, 4884, 6105, 6512, 8140, 8880, 9768, 12210, 16280, 19536, 24420, 32560, 48840, 97680.
What is 97680 in binary?
10111110110010000 (hexadecimal 17D90, octal 276620).
What is the square root of 97680?
About 312.5380, exactly 4√6105.
Is 97680 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 97680?
97680 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.