The number 21728
21728 is a composite number with 24 divisors. Its prime factorisation is × 7 × 97. Divisors (24): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 97, 112, 194, 224, 388, 679 … 21728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21728 is composite. Its prime factorisation is
- 3
The divisors add up to 49392; without 21728 itself that is 27664, so 21728 is abundant (27664 is more than 21728). Euler's totient φ(21728) = 9216 numbers up to 21728 share no factor with it.
- 4
The digits of 21728 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 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21728 = 2^{5} \times 7 \times 97 \]21728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 49392 |
| Euler totient φ(n) | 9216 |
| Square | 472105984 |
| Cube | 10257918820352 |
| Square root | 147.404206 (= 4√1358) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.1728 × |
21728 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and twenty-eight |
| Binary (base 2) | 101010011100000 |
| Octal (base 8) | 52340 |
| Hexadecimal (base 16) | 54E0 |
| Base 3 | 1002210202 |
| As time | 21728 seconds = 6 h 2 min 8 s |
Is 21728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21728 ÷ 2 = 10864) | 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 (21728 ÷ 4 = 5432) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 (21728 ÷ 7 = 3104) | 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 (21728 ÷ 8 = 2716) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 21728 a prime number?
No. 21728 = × 7 × 97, so it is divisible by 2.
What are the factors of 21728?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 97, 112, 194, 224, 388, 679, 776, 1358, 1552, 2716, 3104, 5432, 10864, 21728.
What is 21728 in binary?
101010011100000 (hexadecimal 54E0, octal 52340).
What is the square root of 21728?
About 147.4042, exactly 4√1358.
Is 21728 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 21728?
It is a composite number with 24 divisors.