The number 21888
21888 is a composite number with 48 divisors. Its prime factorisation is × × 19. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48 … 21888.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21888 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21888 is composite. Its prime factorisation is
- 3
The divisors add up to 66300; without 21888 itself that is 44412, so 21888 is abundant (44412 is more than 21888). Euler's totient φ(21888) = 6912 numbers up to 21888 share no factor with it.
- 4
The digits of 21888 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 131 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21888 = 2^{7} \times 3^{2} \times 19 \]21888 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 66300 |
| Euler totient φ(n) | 6912 |
| Square | 479084544 |
| Cube | 10486202499072 |
| Square root | 147.945936 (= 24√38) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 131 |
| Scientific notation | 2.1888 × |
21888 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand eight hundred and eighty-eight |
| Binary (base 2) | 101010110000000 |
| Octal (base 8) | 52600 |
| Hexadecimal (base 16) | 5580 |
| Base 3 | 1010000200 |
| As time | 21888 seconds = 6 h 4 min 48 s |
Is 21888 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21888 ÷ 2 = 10944) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21888 ÷ 3 = 7296) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21888 ÷ 4 = 5472) | 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 (21888 ÷ 6 = 3648) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (21888 ÷ 8 = 2736) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21888 ÷ 9 = 2432) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21888 ÷ 12 = 1824) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21888 a prime number?
No. 21888 = × × 19, so it is divisible by 2.
What are the factors of 21888?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48, 57, 64, 72, 76, 96, 114, 128, 144, 152, 171, 192, 228, 288, 304, 342, 384, 456, 576, 608, 684, 912, 1152, 1216, 1368, 1824, 2432, 2736, 3648, 5472, 7296, 10944, 21888.
What is 21888 in binary?
101010110000000 (hexadecimal 5580, octal 52600).
What is the square root of 21888?
About 147.9459, exactly 24√38.
Is 21888 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 21888?
It is a composite number with 48 divisors.