The number 77280
77280 is a composite number with 96 divisors. Its prime factorisation is × 3 × 5 × 7 × 23. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23 … 77280.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77280: a Harshad number: divisible by its digit sum 24.
- 2
77280 is composite. Its prime factorisation is
- 3
The divisors add up to 290304; without 77280 itself that is 213024, so 77280 is abundant (213024 is more than 77280). Euler's totient φ(77280) = 16896 numbers up to 77280 share no factor with it.
- 4
The digits of 77280 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77280 = 2^{5} \times 3 \times 5 \times 7 \times 23 \]77280 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 290304 |
| Euler totient φ(n) | 16896 |
| Square | 5972198400 |
| Cube | 461531492352000 |
| Square root | 277.992806 (= 4√4830) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.728 × |
77280 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand two hundred and eighty |
| Binary (base 2) | 10010110111100000 |
| Octal (base 8) | 226740 |
| Hexadecimal (base 16) | 12DE0 |
| Base 3 | 10221000020 |
| As time | 77280 seconds = 21 h 28 min 0 s |
Is 77280 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77280 ÷ 2 = 38640) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77280 ÷ 3 = 25760) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77280 ÷ 4 = 19320) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77280 ÷ 5 = 15456) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77280 ÷ 6 = 12880) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77280 ÷ 7 = 11040) | 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 (77280 ÷ 8 = 9660) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77280 ÷ 10 = 7728) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77280 ÷ 12 = 6440) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77280 a prime number?
No. 77280 = × 3 × 5 × 7 × 23, so it is divisible by 2.
What are the factors of 77280?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 32, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 96, 105, 112, 115, 120, 138, 140, 160, 161, 168, 184, 210, 224, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 480, 483, 552, 560, 644, 672, 690, 736, 805, 840, 920, 966, 1104, 1120, 1288, 1380, 1610, 1680, 1840, 1932, 2208, 2415, 2576, 2760, 3220, 3360, 3680, 3864, 4830, 5152, 5520, 6440, 7728, 9660, 11040, 12880, 15456, 19320, 25760, 38640, 77280.
What is 77280 in binary?
10010110111100000 (hexadecimal 12DE0, octal 226740).
What is the square root of 77280?
About 277.9928, exactly 4√4830.
Is 77280 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77280?
77280 is a Harshad number: divisible by its digit sum 24.