The number 87360
87360 is a composite number with 112 divisors. Its prime factorisation is × 3 × 5 × 7 × 13. Divisors (112): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21 … 87360.
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How to work it out
- 1
What is special about 87360: a Harshad number: divisible by its digit sum 24.
- 2
87360 is composite. Its prime factorisation is
- 3
The divisors add up to 341376; without 87360 itself that is 254016, so 87360 is abundant (254016 is more than 87360). Euler's totient φ(87360) = 18432 numbers up to 87360 share no factor with it.
- 4
The digits of 87360 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 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87360 = 2^{6} \times 3 \times 5 \times 7 \times 13 \]87360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 112 |
| Sum of divisors | 341376 |
| Euler totient φ(n) | 18432 |
| Square | 7631769600 |
| Cube | 666711392256000 |
| Square root | 295.567251 (= 8√1365) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 19 |
| Scientific notation | 8.736 × |
87360 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand three hundred and sixty |
| Binary (base 2) | 10101010101000000 |
| Octal (base 8) | 252500 |
| Hexadecimal (base 16) | 15540 |
| Base 3 | 11102211120 |
| As time | 87360 seconds = 24 h 16 min 0 s |
Is 87360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87360 ÷ 2 = 43680) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87360 ÷ 3 = 29120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87360 ÷ 4 = 21840) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (87360 ÷ 5 = 17472) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87360 ÷ 6 = 14560) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (87360 ÷ 7 = 12480) | 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 (87360 ÷ 8 = 10920) | 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 (87360 ÷ 10 = 8736) | 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 (87360 ÷ 12 = 7280) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87360 a prime number?
No. 87360 = × 3 × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 87360?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21, 24, 26, 28, 30, 32, 35, 39, 40, 42, 48, 52, 56, 60, 64, 65, 70, 78, 80, 84, 91, 96, 104, 105, 112, 120, 130, 140, 156, 160, 168, 182, 192, 195, 208, 210, 224, 240, 260, 273, 280, 312, 320, 336, 364, 390, 416, 420, 448, 455, 480, 520, 546, 560, 624, 672, 728, 780, 832, 840, 910, 960, 1040, 1092, 1120, 1248, 1344, 1365, 1456, 1560, 1680, 1820, 2080, 2184, 2240, 2496, 2730, 2912, 3120, 3360, 3640, 4160, 4368, 5460, 5824, 6240, 6720, 7280, 8736, 10920, 12480, 14560, 17472, 21840, 29120, 43680, 87360.
What is 87360 in binary?
10101010101000000 (hexadecimal 15540, octal 252500).
What is the square root of 87360?
About 295.5673, exactly 8√1365.
Is 87360 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 87360?
87360 is a Harshad number: divisible by its digit sum 24.