The number 23424
23424 is a composite number with 32 divisors. Its prime factorisation is × 3 × 61. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 61, 64, 96, 122, 128 … 23424.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23424: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
23424 is composite. Its prime factorisation is
- 3
The divisors add up to 63240; without 23424 itself that is 39816, so 23424 is abundant (39816 is more than 23424). Euler's totient φ(23424) = 7680 numbers up to 23424 share no factor with it.
- 4
The digits of 23424 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 100 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23424 = 2^{7} \times 3 \times 61 \]23424 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 63240 |
| Euler totient φ(n) | 7680 |
| Square | 548683776 |
| Cube | 12852368769024 |
| Square root | 153.049012 (= 8√366) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 100 |
| Scientific notation | 2.3424 × |
23424 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand four hundred and twenty-four |
| Binary (base 2) | 101101110000000 |
| Octal (base 8) | 55600 |
| Hexadecimal (base 16) | 5B80 |
| Base 3 | 1012010120 |
| As time | 23424 seconds = 6 h 30 min 24 s |
Is 23424 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23424 ÷ 2 = 11712) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23424 ÷ 3 = 7808) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23424 ÷ 4 = 5856) | 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 (23424 ÷ 6 = 3904) | 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 | Yes (23424 ÷ 8 = 2928) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23424 ÷ 12 = 1952) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23424 a prime number?
No. 23424 = × 3 × 61, so it is divisible by 2.
What are the factors of 23424?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 61, 64, 96, 122, 128, 183, 192, 244, 366, 384, 488, 732, 976, 1464, 1952, 2928, 3904, 5856, 7808, 11712, 23424.
What is 23424 in binary?
101101110000000 (hexadecimal 5B80, octal 55600).
What is the square root of 23424?
About 153.0490, exactly 8√366.
Is 23424 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 23424?
23424 is a happy number: repeatedly adding the squares of its digits reaches 1.