The number 21744
21744 is a composite number with 30 divisors. Its prime factorisation is × × 151. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 151 … 21744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21744: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
21744 is composite. Its prime factorisation is
- 3
The divisors add up to 61256; without 21744 itself that is 39512, so 21744 is abundant (39512 is more than 21744). Euler's totient φ(21744) = 7200 numbers up to 21744 share no factor with it.
- 4
The digits of 21744 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21744 = 2^{4} \times 3^{2} \times 151 \]21744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 61256 |
| Euler totient φ(n) | 7200 |
| Square | 472801536 |
| Cube | 10280596598784 |
| Square root | 147.458469 (= 12√151) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.1744 × |
21744 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and forty-four |
| Binary (base 2) | 101010011110000 |
| Octal (base 8) | 52360 |
| Hexadecimal (base 16) | 54F0 |
| Base 3 | 1002211100 |
| As time | 21744 seconds = 6 h 2 min 24 s |
Is 21744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21744 ÷ 2 = 10872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21744 ÷ 3 = 7248) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21744 ÷ 4 = 5436) | 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 (21744 ÷ 6 = 3624) | 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 (21744 ÷ 8 = 2718) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21744 ÷ 9 = 2416) | 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 | Yes (21744 ÷ 12 = 1812) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21744 a prime number?
No. 21744 = × × 151, so it is divisible by 2.
What are the factors of 21744?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 151, 302, 453, 604, 906, 1208, 1359, 1812, 2416, 2718, 3624, 5436, 7248, 10872, 21744.
What is 21744 in binary?
101010011110000 (hexadecimal 54F0, octal 52360).
What is the square root of 21744?
About 147.4585, exactly 12√151.
Is 21744 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21744?
21744 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.