The number 20584
20584 is a composite number with 16 divisors. Its prime factorisation is × 31 × 83. Divisors (16): 1, 2, 4, 8, 31, 62, 83, 124, 166, 248, 332, 664, 2573, 5146, 10292, 20584.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20584: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
20584 is composite. Its prime factorisation is
- 3
The divisors add up to 40320; without 20584 itself that is 19736, so 20584 is deficient (19736 is less than 20584). Euler's totient φ(20584) = 9840 numbers up to 20584 share no factor with it.
- 4
The digits of 20584 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20584 = 2^{3} \times 31 \times 83 \]20584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 40320 |
| Euler totient φ(n) | 9840 |
| Square | 423701056 |
| Cube | 8721462536704 |
| Square root | 143.471251 (= 2√5146) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.0584 × |
20584 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand five hundred and eighty-four |
| Binary (base 2) | 101000001101000 |
| Octal (base 8) | 50150 |
| Hexadecimal (base 16) | 5068 |
| Base 3 | 1001020101 |
| As time | 20584 seconds = 5 h 43 min 4 s |
Is 20584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20584 ÷ 2 = 10292) | 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 (20584 ÷ 4 = 5146) | 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 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 (20584 ÷ 8 = 2573) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 20584 a prime number?
No. 20584 = × 31 × 83, so it is divisible by 2.
What are the factors of 20584?
1, 2, 4, 8, 31, 62, 83, 124, 166, 248, 332, 664, 2573, 5146, 10292, 20584.
What is 20584 in binary?
101000001101000 (hexadecimal 5068, octal 50150).
What is the square root of 20584?
About 143.4713, exactly 2√5146.
Is 20584 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 20584?
20584 is a happy number: repeatedly adding the squares of its digits reaches 1.