The number 17964
17964 is a composite number with 18 divisors. Its prime factorisation is × × 499. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 499, 998, 1497, 1996, 2994, 4491, 5988 … 17964.
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How to work it out
- 1
17964 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
17964 is composite. Its prime factorisation is
- 3
The divisors add up to 45500; without 17964 itself that is 27536, so 17964 is abundant (27536 is more than 17964). Euler's totient φ(17964) = 5976 numbers up to 17964 share no factor with it.
- 4
The digits of 17964 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 185 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17964 = 2^{2} \times 3^{2} \times 499 \]17964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 45500 |
| Euler totient φ(n) | 5976 |
| Square | 322705296 |
| Cube | 5797077937344 |
| Square root | 134.029847 (= 6√499) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 185 |
| Scientific notation | 1.7964 × |
17964 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and sixty-four |
| Binary (base 2) | 100011000101100 |
| Octal (base 8) | 43054 |
| Hexadecimal (base 16) | 462C |
| Base 3 | 220122100 |
| As time | 17964 seconds = 4 h 59 min 24 s |
Is 17964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17964 ÷ 2 = 8982) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17964 ÷ 3 = 5988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17964 ÷ 4 = 4491) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17964 ÷ 6 = 2994) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (17964 ÷ 9 = 1996) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 (17964 ÷ 12 = 1497) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17964 a prime number?
No. 17964 = × × 499, so it is divisible by 2.
What are the factors of 17964?
1, 2, 3, 4, 6, 9, 12, 18, 36, 499, 998, 1497, 1996, 2994, 4491, 5988, 8982, 17964.
What is 17964 in binary?
100011000101100 (hexadecimal 462C, octal 43054).
What is the square root of 17964?
About 134.0298, exactly 6√499.
Is 17964 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 17964?
It is a composite number with 18 divisors.