The number 17982
17982 is a composite number with 24 divisors. Its prime factorisation is 2 × × 37. Divisors (24): 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 243, 333 … 17982.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17982: a Harshad number: divisible by its digit sum 27.
- 2
17982 is composite. Its prime factorisation is
- 3
The divisors add up to 41496; without 17982 itself that is 23514, so 17982 is abundant (23514 is more than 17982). Euler's totient φ(17982) = 5832 numbers up to 17982 share no factor with it.
- 4
The digits of 17982 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 141 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17982 = 2 \times 3^{5} \times 37 \]17982 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 41496 |
| Euler totient φ(n) | 5832 |
| Square | 323352324 |
| Cube | 5814521490168 |
| Square root | 134.096980 (= 9√222) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 141 |
| Scientific notation | 1.7982 × |
17982 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and eighty-two |
| Binary (base 2) | 100011000111110 |
| Octal (base 8) | 43076 |
| Hexadecimal (base 16) | 463E |
| Base 3 | 220200000 |
| As time | 17982 seconds = 4 h 59 min 42 s |
Is 17982 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17982 ÷ 2 = 8991) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17982 ÷ 3 = 5994) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17982 ÷ 6 = 2997) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (17982 ÷ 9 = 1998) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17982 a prime number?
No. 17982 = 2 × × 37, so it is divisible by 2.
What are the factors of 17982?
1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 243, 333, 486, 666, 999, 1998, 2997, 5994, 8991, 17982.
What is 17982 in binary?
100011000111110 (hexadecimal 463E, octal 43076).
What is the square root of 17982?
About 134.0970, exactly 9√222.
Is 17982 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 17982?
17982 is a Harshad number: divisible by its digit sum 27.