The number 23664
23664 is a composite number with 40 divisors. Its prime factorisation is × 3 × 17 × 29. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 29, 34, 48, 51, 58, 68 … 23664.
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How to work it out
- 1
23664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
23664 is composite. Its prime factorisation is
- 3
The divisors add up to 66960; without 23664 itself that is 43296, so 23664 is abundant (43296 is more than 23664). Euler's totient φ(23664) = 7168 numbers up to 23664 share no factor with it.
- 4
The digits of 23664 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 100 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23664 = 2^{4} \times 3 \times 17 \times 29 \]23664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 66960 |
| Euler totient φ(n) | 7168 |
| Square | 559984896 |
| Cube | 13251482578944 |
| Square root | 153.831076 (= 4√1479) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 100 |
| Scientific notation | 2.3664 × |
23664 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand six hundred and sixty-four |
| Binary (base 2) | 101110001110000 |
| Octal (base 8) | 56160 |
| Hexadecimal (base 16) | 5C70 |
| Base 3 | 1012110110 |
| As time | 23664 seconds = 6 h 34 min 24 s |
Is 23664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23664 ÷ 2 = 11832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23664 ÷ 3 = 7888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23664 ÷ 4 = 5916) | 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 (23664 ÷ 6 = 3944) | 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 | Yes (23664 ÷ 8 = 2958) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23664 ÷ 12 = 1972) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23664 a prime number?
No. 23664 = × 3 × 17 × 29, so it is divisible by 2.
What are the factors of 23664?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 29, 34, 48, 51, 58, 68, 87, 102, 116, 136, 174, 204, 232, 272, 348, 408, 464, 493, 696, 816, 986, 1392, 1479, 1972, 2958, 3944, 5916, 7888, 11832, 23664.
What is 23664 in binary?
101110001110000 (hexadecimal 5C70, octal 56160).
What is the square root of 23664?
About 153.8311, exactly 4√1479.
Is 23664 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 23664?
It is a composite number with 40 divisors.