The number 20800
20800 is a composite number with 42 divisors. Its prime factorisation is × × 13. Divisors (42): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64 … 20800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20800: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
20800 is composite. Its prime factorisation is
- 3
The divisors add up to 55118; without 20800 itself that is 34318, so 20800 is abundant (34318 is more than 20800). Euler's totient φ(20800) = 7680 numbers up to 20800 share no factor with it.
- 4
The digits of 20800 add up to 10, 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
\[ 20800 = 2^{6} \times 5^{2} \times 13 \]20800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 55118 |
| Euler totient φ(n) | 7680 |
| Square | 432640000 |
| Cube | 8998912000000 |
| Square root | 144.222051 (= 40√13) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.08 × |
20800 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand eight hundred |
| Binary (base 2) | 101000101000000 |
| Octal (base 8) | 50500 |
| Hexadecimal (base 16) | 5140 |
| Base 3 | 1001112101 |
| As time | 20800 seconds = 5 h 46 min 40 s |
Is 20800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20800 ÷ 2 = 10400) | 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 (20800 ÷ 4 = 5200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20800 ÷ 5 = 4160) | 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 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 (20800 ÷ 8 = 2600) | 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 | Yes (20800 ÷ 10 = 2080) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 20800 a prime number?
No. 20800 = × × 13, so it is divisible by 2.
What are the factors of 20800?
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 130, 160, 200, 208, 260, 320, 325, 400, 416, 520, 650, 800, 832, 1040, 1300, 1600, 2080, 2600, 4160, 5200, 10400, 20800.
What is 20800 in binary?
101000101000000 (hexadecimal 5140, octal 50500).
What is the square root of 20800?
About 144.2221, exactly 40√13.
Is 20800 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 20800?
20800 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.