The number 23744
23744 is a composite number with 28 divisors. Its prime factorisation is × 7 × 53. Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 32, 53, 56, 64, 106, 112, 212, 224 … 23744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23744: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
23744 is composite. Its prime factorisation is
- 3
The divisors add up to 54864; without 23744 itself that is 31120, so 23744 is abundant (31120 is more than 23744). Euler's totient φ(23744) = 9984 numbers up to 23744 share no factor with it.
- 4
The digits of 23744 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23744 = 2^{6} \times 7 \times 53 \]23744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 54864 |
| Euler totient φ(n) | 9984 |
| Square | 563777536 |
| Cube | 13386333814784 |
| Square root | 154.090882 (= 8√371) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3744 × |
23744 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand seven hundred and forty-four |
| Binary (base 2) | 101110011000000 |
| Octal (base 8) | 56300 |
| Hexadecimal (base 16) | 5CC0 |
| Base 3 | 1012120102 |
| As time | 23744 seconds = 6 h 35 min 44 s |
Is 23744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23744 ÷ 2 = 11872) | 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 (23744 ÷ 4 = 5936) | 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 | Yes (23744 ÷ 7 = 3392) | 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 (23744 ÷ 8 = 2968) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 6) | 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 23744 a prime number?
No. 23744 = × 7 × 53, so it is divisible by 2.
What are the factors of 23744?
1, 2, 4, 7, 8, 14, 16, 28, 32, 53, 56, 64, 106, 112, 212, 224, 371, 424, 448, 742, 848, 1484, 1696, 2968, 3392, 5936, 11872, 23744.
What is 23744 in binary?
101110011000000 (hexadecimal 5CC0, octal 56300).
What is the square root of 23744?
About 154.0909, exactly 8√371.
Is 23744 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 23744?
23744 is a happy number: repeatedly adding the squares of its digits reaches 1.