The number 21904
21904 is a perfect square (148²). Its prime factorisation is × . Divisors (15): 1, 2, 4, 8, 16, 37, 74, 148, 296, 592, 1369, 2738, 5476, 10952, 21904.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21904: a perfect square (148²); a Harshad number: divisible by its digit sum 16.
- 2
21904 is composite. Its prime factorisation is
- 3
The divisors add up to 43617; without 21904 itself that is 21713, so 21904 is deficient (21713 is less than 21904). Euler's totient φ(21904) = 10656 numbers up to 21904 share no factor with it.
- 4
The digits of 21904 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21904 = 2^{4} \times 37^{2} \]21904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 43617 |
| Euler totient φ(n) | 10656 |
| Square | 479785216 |
| Cube | 10509215371264 |
| Square root | 148 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 43 |
| Scientific notation | 2.1904 × |
| Perfect power |
21904 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and four |
| Binary (base 2) | 101010110010000 |
| Octal (base 8) | 52620 |
| Hexadecimal (base 16) | 5590 |
| Base 3 | 1010001021 |
| As time | 21904 seconds = 6 h 5 min 4 s |
Is 21904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21904 ÷ 2 = 10952) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21904 ÷ 4 = 5476) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (21904 ÷ 8 = 2738) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21904 a prime number?
No. 21904 = × , so it is divisible by 2.
What are the factors of 21904?
1, 2, 4, 8, 16, 37, 74, 148, 296, 592, 1369, 2738, 5476, 10952, 21904.
What is 21904 in binary?
101010110010000 (hexadecimal 5590, octal 52620).
What is the square root of 21904?
148, because 148 × 148 = 21904.
Is 21904 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 21904?
21904 is a perfect square (148²); a Harshad number: divisible by its digit sum 16.