The number 17680
17680 is a composite number with 40 divisors. Its prime factorisation is × 5 × 13 × 17. Divisors (40): 1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 26, 34, 40, 52, 65, 68 … 17680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
17680 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
17680 is composite. Its prime factorisation is
- 3
The divisors add up to 46872; without 17680 itself that is 29192, so 17680 is abundant (29192 is more than 17680). Euler's totient φ(17680) = 6144 numbers up to 17680 share no factor with it.
- 4
The digits of 17680 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 97 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17680 = 2^{4} \times 5 \times 13 \times 17 \]17680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 46872 |
| Euler totient φ(n) | 6144 |
| Square | 312582400 |
| Cube | 5526456832000 |
| Square root | 132.966161 (= 4√1105) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 97 |
| Scientific notation | 1.768 × |
17680 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand six hundred and eighty |
| Binary (base 2) | 100010100010000 |
| Octal (base 8) | 42420 |
| Hexadecimal (base 16) | 4510 |
| Base 3 | 220020211 |
| As time | 17680 seconds = 4 h 54 min 40 s |
Is 17680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17680 ÷ 2 = 8840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17680 ÷ 4 = 4420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17680 ÷ 5 = 3536) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (17680 ÷ 8 = 2210) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17680 ÷ 10 = 1768) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17680 a prime number?
No. 17680 = × 5 × 13 × 17, so it is divisible by 2.
What are the factors of 17680?
1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 26, 34, 40, 52, 65, 68, 80, 85, 104, 130, 136, 170, 208, 221, 260, 272, 340, 442, 520, 680, 884, 1040, 1105, 1360, 1768, 2210, 3536, 4420, 8840, 17680.
What is 17680 in binary?
100010100010000 (hexadecimal 4510, octal 42420).
What is the square root of 17680?
About 132.9662, exactly 4√1105.
Is 17680 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 17680?
It is a composite number with 40 divisors.