The number 77760
77760 is a composite number with 84 divisors. Its prime factorisation is × × 5. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 77760.
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How to work it out
- 1
What is special about 77760: a Harshad number: divisible by its digit sum 27.
- 2
77760 is composite. Its prime factorisation is
- 3
The divisors add up to 277368; without 77760 itself that is 199608, so 77760 is abundant (199608 is more than 77760). Euler's totient φ(77760) = 20736 numbers up to 77760 share no factor with it.
- 4
The digits of 77760 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77760 = 2^{6} \times 3^{5} \times 5 \]77760 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 277368 |
| Euler totient φ(n) | 20736 |
| Square | 6046617600 |
| Cube | 470184984576000 |
| Square root | 278.854801 (= 72√15) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.776 × |
77760 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and sixty |
| Binary (base 2) | 10010111111000000 |
| Octal (base 8) | 227700 |
| Hexadecimal (base 16) | 12FC0 |
| Base 3 | 10221200000 |
| As time | 77760 seconds = 21 h 36 min 0 s |
Is 77760 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77760 ÷ 2 = 38880) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77760 ÷ 3 = 25920) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77760 ÷ 4 = 19440) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77760 ÷ 5 = 15552) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77760 ÷ 6 = 12960) | 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 (77760 ÷ 8 = 9720) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77760 ÷ 9 = 8640) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77760 ÷ 10 = 7776) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77760 ÷ 12 = 6480) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77760 a prime number?
No. 77760 = × × 5, so it is divisible by 2.
What are the factors of 77760?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 81, 90, 96, 108, 120, 135, 144, 160, 162, 180, 192, 216, 240, 243, 270, 288, 320, 324, 360, 405, 432, 480, 486, 540, 576, 648, 720, 810, 864, 960, 972, 1080, 1215, 1296, 1440, 1620, 1728, 1944, 2160, 2430, 2592, 2880, 3240, 3888, 4320, 4860, 5184, 6480, 7776, 8640, 9720, 12960, 15552, 19440, 25920, 38880, 77760.
What is 77760 in binary?
10010111111000000 (hexadecimal 12FC0, octal 227700).
What is the square root of 77760?
About 278.8548, exactly 72√15.
Is 77760 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77760?
77760 is a Harshad number: divisible by its digit sum 27.