The number 17980
17980 is a composite number with 24 divisors. Its prime factorisation is × 5 × 29 × 31. Divisors (24): 1, 2, 4, 5, 10, 20, 29, 31, 58, 62, 116, 124, 145, 155, 290, 310 … 17980.
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How to work it out
- 1
17980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
17980 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 17980 itself that is 22340, so 17980 is abundant (22340 is more than 17980). Euler's totient φ(17980) = 6720 numbers up to 17980 share no factor with it.
- 4
The digits of 17980 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 79 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17980 = 2^{2} \times 5 \times 29 \times 31 \]17980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 6720 |
| Square | 323280400 |
| Cube | 5812581592000 |
| Square root | 134.089522 (= 2√4495) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 79 |
| Scientific notation | 1.798 × |
17980 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and eighty |
| Binary (base 2) | 100011000111100 |
| Octal (base 8) | 43074 |
| Hexadecimal (base 16) | 463C |
| Base 3 | 220122221 |
| As time | 17980 seconds = 4 h 59 min 40 s |
Is 17980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17980 ÷ 2 = 8990) | 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 (17980 ÷ 4 = 4495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17980 ÷ 5 = 3596) | 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 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17980 ÷ 10 = 1798) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 17980 a prime number?
No. 17980 = × 5 × 29 × 31, so it is divisible by 2.
What are the factors of 17980?
1, 2, 4, 5, 10, 20, 29, 31, 58, 62, 116, 124, 145, 155, 290, 310, 580, 620, 899, 1798, 3596, 4495, 8990, 17980.
What is 17980 in binary?
100011000111100 (hexadecimal 463C, octal 43074).
What is the square root of 17980?
About 134.0895, exactly 2√4495.
Is 17980 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 17980?
It is a composite number with 24 divisors.