The number 20784
20784 is a composite number with 20 divisors. Its prime factorisation is × 3 × 433. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 433, 866, 1299, 1732, 2598, 3464 … 20784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20784: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
20784 is composite. Its prime factorisation is
- 3
The divisors add up to 53816; without 20784 itself that is 33032, so 20784 is abundant (33032 is more than 20784). Euler's totient φ(20784) = 6912 numbers up to 20784 share no factor with it.
- 4
The digits of 20784 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 149 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20784 = 2^{4} \times 3 \times 433 \]20784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 53816 |
| Euler totient φ(n) | 6912 |
| Square | 431974656 |
| Cube | 8978161250304 |
| Square root | 144.166570 (= 4√1299) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 149 |
| Scientific notation | 2.0784 × |
20784 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand seven hundred and eighty-four |
| Binary (base 2) | 101000100110000 |
| Octal (base 8) | 50460 |
| Hexadecimal (base 16) | 5130 |
| Base 3 | 1001111210 |
| As time | 20784 seconds = 5 h 46 min 24 s |
Is 20784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20784 ÷ 2 = 10392) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20784 ÷ 3 = 6928) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20784 ÷ 4 = 5196) | 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 | Yes (20784 ÷ 6 = 3464) | 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 (20784 ÷ 8 = 2598) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (20784 ÷ 12 = 1732) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20784 a prime number?
No. 20784 = × 3 × 433, so it is divisible by 2.
What are the factors of 20784?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 433, 866, 1299, 1732, 2598, 3464, 5196, 6928, 10392, 20784.
What is 20784 in binary?
101000100110000 (hexadecimal 5130, octal 50460).
What is the square root of 20784?
About 144.1666, exactly 4√1299.
Is 20784 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 20784?
20784 is a happy number: repeatedly adding the squares of its digits reaches 1.