The number 43680
43680 is a composite number with 96 divisors. Its prime factorisation is × 3 × 5 × 7 × 13. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 21 … 43680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 43680: a Harshad number: divisible by its digit sum 21.
- 2
43680 is composite. Its prime factorisation is
- 3
The divisors add up to 169344; without 43680 itself that is 125664, so 43680 is abundant (125664 is more than 43680). Euler's totient φ(43680) = 9216 numbers up to 43680 share no factor with it.
- 4
The digits of 43680 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 18 steps to reach 1.
LaTeX source of the formulas on this page
\[ 43680 = 2^{5} \times 3 \times 5 \times 7 \times 13 \]43680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 169344 |
| Euler totient φ(n) | 9216 |
| Square | 1907942400 |
| Cube | 83338924032000 |
| Square root | 208.997608 (= 4√2730) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 18 |
| Scientific notation | 4.368 × |
43680 in other forms
| Form | Value |
|---|---|
| In words | forty-three thousand six hundred and eighty |
| Binary (base 2) | 1010101010100000 |
| Octal (base 8) | 125240 |
| Hexadecimal (base 16) | AAA0 |
| Base 3 | 2012220210 |
| As time | 43680 seconds = 12 h 8 min 0 s |
Is 43680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (43680 ÷ 2 = 21840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (43680 ÷ 3 = 14560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (43680 ÷ 4 = 10920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (43680 ÷ 5 = 8736) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (43680 ÷ 6 = 7280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (43680 ÷ 7 = 6240) | 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 (43680 ÷ 8 = 5460) | 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 (43680 ÷ 10 = 4368) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (43680 ÷ 12 = 3640) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 43680 a prime number?
No. 43680 = × 3 × 5 × 7 × 13, so it is divisible by 2.
What are the factors of 43680?
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, 65, 70, 78, 80, 84, 91, 96, 104, 105, 112, 120, 130, 140, 156, 160, 168, 182, 195, 208, 210, 224, 240, 260, 273, 280, 312, 336, 364, 390, 416, 420, 455, 480, 520, 546, 560, 624, 672, 728, 780, 840, 910, 1040, 1092, 1120, 1248, 1365, 1456, 1560, 1680, 1820, 2080, 2184, 2730, 2912, 3120, 3360, 3640, 4368, 5460, 6240, 7280, 8736, 10920, 14560, 21840, 43680.
What is 43680 in binary?
1010101010100000 (hexadecimal AAA0, octal 125240).
What is the square root of 43680?
About 208.9976, exactly 4√2730.
Is 43680 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 43680?
43680 is a Harshad number: divisible by its digit sum 21.