The number 17664
17664 is a composite number with 36 divisors. Its prime factorisation is × 3 × 23. Divisors (36): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 64, 69, 92 … 17664.
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How to work it out
- 1
What is special about 17664: a Harshad number: divisible by its digit sum 24.
- 2
17664 is composite. Its prime factorisation is
- 3
The divisors add up to 49056; without 17664 itself that is 31392, so 17664 is abundant (31392 is more than 17664). Euler's totient φ(17664) = 5632 numbers up to 17664 share no factor with it.
- 4
The digits of 17664 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 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17664 = 2^{8} \times 3 \times 23 \]17664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 49056 |
| Euler totient φ(n) | 5632 |
| Square | 312016896 |
| Cube | 5511466450944 |
| Square root | 132.905982 (= 16√69) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 22 |
| Scientific notation | 1.7664 × |
17664 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand six hundred and sixty-four |
| Binary (base 2) | 100010100000000 |
| Octal (base 8) | 42400 |
| Hexadecimal (base 16) | 4500 |
| Base 3 | 220020020 |
| As time | 17664 seconds = 4 h 54 min 24 s |
Is 17664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17664 ÷ 2 = 8832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17664 ÷ 3 = 5888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17664 ÷ 4 = 4416) | 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 (17664 ÷ 6 = 2944) | 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 (17664 ÷ 8 = 2208) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (17664 ÷ 12 = 1472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17664 a prime number?
No. 17664 = × 3 × 23, so it is divisible by 2.
What are the factors of 17664?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 64, 69, 92, 96, 128, 138, 184, 192, 256, 276, 368, 384, 552, 736, 768, 1104, 1472, 2208, 2944, 4416, 5888, 8832, 17664.
What is 17664 in binary?
100010100000000 (hexadecimal 4500, octal 42400).
What is the square root of 17664?
About 132.9060, exactly 16√69.
Is 17664 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 17664?
17664 is a Harshad number: divisible by its digit sum 24.