The number 21696
21696 is a composite number with 28 divisors. Its prime factorisation is × 3 × 113. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 192, 226 … 21696.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21696: a Harshad number: divisible by its digit sum 24.
- 2
21696 is composite. Its prime factorisation is
- 3
The divisors add up to 57912; without 21696 itself that is 36216, so 21696 is abundant (36216 is more than 21696). Euler's totient φ(21696) = 7168 numbers up to 21696 share no factor with it.
- 4
The digits of 21696 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21696 = 2^{6} \times 3 \times 113 \]21696 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 57912 |
| Euler totient φ(n) | 7168 |
| Square | 470716416 |
| Cube | 10212663361536 |
| Square root | 147.295621 (= 8√339) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1696 × |
21696 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand six hundred and ninety-six |
| Binary (base 2) | 101010011000000 |
| Octal (base 8) | 52300 |
| Hexadecimal (base 16) | 54C0 |
| Base 3 | 1002202120 |
| As time | 21696 seconds = 6 h 1 min 36 s |
Is 21696 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21696 ÷ 2 = 10848) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21696 ÷ 3 = 7232) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21696 ÷ 4 = 5424) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21696 ÷ 6 = 3616) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (21696 ÷ 8 = 2712) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21696 ÷ 12 = 1808) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21696 a prime number?
No. 21696 = × 3 × 113, so it is divisible by 2.
What are the factors of 21696?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 113, 192, 226, 339, 452, 678, 904, 1356, 1808, 2712, 3616, 5424, 7232, 10848, 21696.
What is 21696 in binary?
101010011000000 (hexadecimal 54C0, octal 52300).
What is the square root of 21696?
About 147.2956, exactly 8√339.
Is 21696 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 21696?
21696 is a Harshad number: divisible by its digit sum 24.