The number 19680
19680 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 41. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 19680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19680: a Harshad number: divisible by its digit sum 24.
- 2
19680 is composite. Its prime factorisation is
- 3
The divisors add up to 63504; without 19680 itself that is 43824, so 19680 is abundant (43824 is more than 19680). Euler's totient φ(19680) = 5120 numbers up to 19680 share no factor with it.
- 4
The digits of 19680 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 74 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19680 = 2^{5} \times 3 \times 5 \times 41 \]19680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 63504 |
| Euler totient φ(n) | 5120 |
| Square | 387302400 |
| Cube | 7622111232000 |
| Square root | 140.285423 (= 4√1230) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 74 |
| Scientific notation | 1.968 × |
19680 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand six hundred and eighty |
| Binary (base 2) | 100110011100000 |
| Octal (base 8) | 46340 |
| Hexadecimal (base 16) | 4CE0 |
| Base 3 | 222222220 |
| As time | 19680 seconds = 5 h 28 min 0 s |
Is 19680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19680 ÷ 2 = 9840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19680 ÷ 3 = 6560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19680 ÷ 4 = 4920) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19680 ÷ 5 = 3936) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (19680 ÷ 6 = 3280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (19680 ÷ 8 = 2460) | 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 (19680 ÷ 10 = 1968) | 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 (19680 ÷ 12 = 1640) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19680 a prime number?
No. 19680 = × 3 × 5 × 41, so it is divisible by 2.
What are the factors of 19680?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 80, 82, 96, 120, 123, 160, 164, 205, 240, 246, 328, 410, 480, 492, 615, 656, 820, 984, 1230, 1312, 1640, 1968, 2460, 3280, 3936, 4920, 6560, 9840, 19680.
What is 19680 in binary?
100110011100000 (hexadecimal 4CE0, octal 46340).
What is the square root of 19680?
About 140.2854, exactly 4√1230.
Is 19680 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 19680?
19680 is a Harshad number: divisible by its digit sum 24.