The number 23504
23504 is a composite number with 20 divisors. Its prime factorisation is × 13 × 113. Divisors (20): 1, 2, 4, 8, 13, 16, 26, 52, 104, 113, 208, 226, 452, 904, 1469, 1808 … 23504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
23504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
23504 is composite. Its prime factorisation is
- 3
The divisors add up to 49476; without 23504 itself that is 25972, so 23504 is abundant (25972 is more than 23504). Euler's totient φ(23504) = 10752 numbers up to 23504 share no factor with it.
- 4
The digits of 23504 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23504 = 2^{4} \times 13 \times 113 \]23504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 49476 |
| Euler totient φ(n) | 10752 |
| Square | 552438016 |
| Cube | 12984503128064 |
| Square root | 153.310143 (= 4√1469) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3504 × |
23504 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand five hundred and four |
| Binary (base 2) | 101101111010000 |
| Octal (base 8) | 55720 |
| Hexadecimal (base 16) | 5BD0 |
| Base 3 | 1012020112 |
| As time | 23504 seconds = 6 h 31 min 44 s |
Is 23504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23504 ÷ 2 = 11752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23504 ÷ 4 = 5876) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (23504 ÷ 8 = 2938) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23504 a prime number?
No. 23504 = × 13 × 113, so it is divisible by 2.
What are the factors of 23504?
1, 2, 4, 8, 13, 16, 26, 52, 104, 113, 208, 226, 452, 904, 1469, 1808, 2938, 5876, 11752, 23504.
What is 23504 in binary?
101101111010000 (hexadecimal 5BD0, octal 55720).
What is the square root of 23504?
About 153.3101, exactly 4√1469.
Is 23504 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 23504?
It is a composite number with 20 divisors.