The number 20688
20688 is a composite number with 20 divisors. Its prime factorisation is × 3 × 431. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 431, 862, 1293, 1724, 2586, 3448 … 20688.
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How to work it out
- 1
What is special about 20688: a Harshad number: divisible by its digit sum 24.
- 2
20688 is composite. Its prime factorisation is
- 3
The divisors add up to 53568; without 20688 itself that is 32880, so 20688 is abundant (32880 is more than 20688). Euler's totient φ(20688) = 6880 numbers up to 20688 share no factor with it.
- 4
The digits of 20688 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 105 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20688 = 2^{4} \times 3 \times 431 \]20688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 53568 |
| Euler totient φ(n) | 6880 |
| Square | 427993344 |
| Cube | 8854326300672 |
| Square root | 143.833237 (= 4√1293) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 105 |
| Scientific notation | 2.0688 × |
20688 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand six hundred and eighty-eight |
| Binary (base 2) | 101000011010000 |
| Octal (base 8) | 50320 |
| Hexadecimal (base 16) | 50D0 |
| Base 3 | 1001101020 |
| As time | 20688 seconds = 5 h 44 min 48 s |
Is 20688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20688 ÷ 2 = 10344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20688 ÷ 3 = 6896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20688 ÷ 4 = 5172) | 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 (20688 ÷ 6 = 3448) | 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 (20688 ÷ 8 = 2586) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (20688 ÷ 12 = 1724) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20688 a prime number?
No. 20688 = × 3 × 431, so it is divisible by 2.
What are the factors of 20688?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 431, 862, 1293, 1724, 2586, 3448, 5172, 6896, 10344, 20688.
What is 20688 in binary?
101000011010000 (hexadecimal 50D0, octal 50320).
What is the square root of 20688?
About 143.8332, exactly 4√1293.
Is 20688 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 20688?
20688 is a Harshad number: divisible by its digit sum 24.