The number 23712
23712 is a composite number with 48 divisors. Its prime factorisation is × 3 × 13 × 19. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 16, 19, 24, 26, 32, 38, 39, 48 … 23712.
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How to work it out
- 1
23712 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
23712 is composite. Its prime factorisation is
- 3
The divisors add up to 70560; without 23712 itself that is 46848, so 23712 is abundant (46848 is more than 23712). Euler's totient φ(23712) = 6912 numbers up to 23712 share no factor with it.
- 4
The digits of 23712 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23712 = 2^{5} \times 3 \times 13 \times 19 \]23712 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 70560 |
| Euler totient φ(n) | 6912 |
| Square | 562258944 |
| Cube | 13332284080128 |
| Square root | 153.987012 (= 4√1482) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3712 × |
23712 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand seven hundred and twelve |
| Binary (base 2) | 101110010100000 |
| Octal (base 8) | 56240 |
| Hexadecimal (base 16) | 5CA0 |
| Base 3 | 1012112020 |
| As time | 23712 seconds = 6 h 35 min 12 s |
Is 23712 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23712 ÷ 2 = 11856) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23712 ÷ 3 = 7904) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23712 ÷ 4 = 5928) | 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 (23712 ÷ 6 = 3952) | 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 (23712 ÷ 8 = 2964) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23712 ÷ 12 = 1976) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23712 a prime number?
No. 23712 = × 3 × 13 × 19, so it is divisible by 2.
What are the factors of 23712?
1, 2, 3, 4, 6, 8, 12, 13, 16, 19, 24, 26, 32, 38, 39, 48, 52, 57, 76, 78, 96, 104, 114, 152, 156, 208, 228, 247, 304, 312, 416, 456, 494, 608, 624, 741, 912, 988, 1248, 1482, 1824, 1976, 2964, 3952, 5928, 7904, 11856, 23712.
What is 23712 in binary?
101110010100000 (hexadecimal 5CA0, octal 56240).
What is the square root of 23712?
About 153.9870, exactly 4√1482.
Is 23712 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 23712?
It is a composite number with 48 divisors.