The number 20640
20640 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 43. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 20640.
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How to work it out
- 1
What is special about 20640: a Harshad number: divisible by its digit sum 12.
- 2
20640 is composite. Its prime factorisation is
- 3
The divisors add up to 66528; without 20640 itself that is 45888, so 20640 is abundant (45888 is more than 20640). Euler's totient φ(20640) = 5376 numbers up to 20640 share no factor with it.
- 4
The digits of 20640 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 105 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20640 = 2^{5} \times 3 \times 5 \times 43 \]20640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 66528 |
| Euler totient φ(n) | 5376 |
| Square | 426009600 |
| Cube | 8792838144000 |
| Square root | 143.666280 (= 4√1290) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 105 |
| Scientific notation | 2.064 × |
20640 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand six hundred and forty |
| Binary (base 2) | 101000010100000 |
| Octal (base 8) | 50240 |
| Hexadecimal (base 16) | 50A0 |
| Base 3 | 1001022110 |
| As time | 20640 seconds = 5 h 44 min 0 s |
Is 20640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20640 ÷ 2 = 10320) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20640 ÷ 3 = 6880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20640 ÷ 4 = 5160) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20640 ÷ 5 = 4128) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20640 ÷ 6 = 3440) | 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 (20640 ÷ 8 = 2580) | 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 | Yes (20640 ÷ 10 = 2064) | 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 (20640 ÷ 12 = 1720) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20640 a prime number?
No. 20640 = × 3 × 5 × 43, so it is divisible by 2.
What are the factors of 20640?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 43, 48, 60, 80, 86, 96, 120, 129, 160, 172, 215, 240, 258, 344, 430, 480, 516, 645, 688, 860, 1032, 1290, 1376, 1720, 2064, 2580, 3440, 4128, 5160, 6880, 10320, 20640.
What is 20640 in binary?
101000010100000 (hexadecimal 50A0, octal 50240).
What is the square root of 20640?
About 143.6663, exactly 4√1290.
Is 20640 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 20640?
20640 is a Harshad number: divisible by its digit sum 12.