The number 21648
21648 is a composite number with 40 divisors. Its prime factorisation is × 3 × 11 × 41. Divisors (40): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 41, 44, 48, 66 … 21648.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21648 is composite. Its prime factorisation is
- 3
The divisors add up to 62496; without 21648 itself that is 40848, so 21648 is abundant (40848 is more than 21648). Euler's totient φ(21648) = 6400 numbers up to 21648 share no factor with it.
- 4
The digits of 21648 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21648 = 2^{4} \times 3 \times 11 \times 41 \]21648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 62496 |
| Euler totient φ(n) | 6400 |
| Square | 468635904 |
| Cube | 10145030049792 |
| Square root | 147.132593 (= 4√1353) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.1648 × |
21648 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred and forty-eight |
| Binary (base 2) | 101010010010000 |
| Octal (base 8) | 52220 |
| Hexadecimal (base 16) | 5490 |
| Base 3 | 1002200210 |
| As time | 21648 seconds = 6 h 0 min 48 s |
Is 21648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21648 ÷ 2 = 10824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21648 ÷ 3 = 7216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21648 ÷ 4 = 5412) | 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 | Yes (21648 ÷ 6 = 3608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (21648 ÷ 8 = 2706) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (21648 ÷ 11 = 1968) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21648 ÷ 12 = 1804) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21648 a prime number?
No. 21648 = × 3 × 11 × 41, so it is divisible by 2.
What are the factors of 21648?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 41, 44, 48, 66, 82, 88, 123, 132, 164, 176, 246, 264, 328, 451, 492, 528, 656, 902, 984, 1353, 1804, 1968, 2706, 3608, 5412, 7216, 10824, 21648.
What is 21648 in binary?
101010010010000 (hexadecimal 5490, octal 52220).
What is the square root of 21648?
About 147.1326, exactly 4√1353.
Is 21648 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 21648?
It is a composite number with 40 divisors.