The number 13680
13680 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 19. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24 … 13680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13680: a Harshad number: divisible by its digit sum 18.
- 2
13680 is composite. Its prime factorisation is
- 3
The divisors add up to 48360; without 13680 itself that is 34680, so 13680 is abundant (34680 is more than 13680). Euler's totient φ(13680) = 3456 numbers up to 13680 share no factor with it.
- 4
The digits of 13680 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13680 = 2^{4} \times 3^{2} \times 5 \times 19 \]13680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 48360 |
| Euler totient φ(n) | 3456 |
| Square | 187142400 |
| Cube | 2560108032000 |
| Square root | 116.961532 (= 12√95) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.368 × |
13680 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and eighty |
| Binary (base 2) | 11010101110000 |
| Octal (base 8) | 32560 |
| Hexadecimal (base 16) | 3570 |
| Base 3 | 200202200 |
| As time | 13680 seconds = 3 h 48 min 0 s |
Is 13680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13680 ÷ 2 = 6840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13680 ÷ 3 = 4560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13680 ÷ 4 = 3420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13680 ÷ 5 = 2736) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13680 ÷ 6 = 2280) | 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 (13680 ÷ 8 = 1710) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13680 ÷ 9 = 1520) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13680 ÷ 10 = 1368) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13680 ÷ 12 = 1140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13680 a prime number?
No. 13680 = × × 5 × 19, so it is divisible by 2.
What are the factors of 13680?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 36, 38, 40, 45, 48, 57, 60, 72, 76, 80, 90, 95, 114, 120, 144, 152, 171, 180, 190, 228, 240, 285, 304, 342, 360, 380, 456, 570, 684, 720, 760, 855, 912, 1140, 1368, 1520, 1710, 2280, 2736, 3420, 4560, 6840, 13680.
What is 13680 in binary?
11010101110000 (hexadecimal 3570, octal 32560).
What is the square root of 13680?
About 116.9615, exactly 12√95.
Is 13680 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13680?
13680 is a Harshad number: divisible by its digit sum 18.