The number 20080
20080 is a composite number with 20 divisors. Its prime factorisation is × 5 × 251. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 251, 502, 1004, 1255, 2008, 2510 … 20080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20080: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
20080 is composite. Its prime factorisation is
- 3
The divisors add up to 46872; without 20080 itself that is 26792, so 20080 is abundant (26792 is more than 20080). Euler's totient φ(20080) = 8000 numbers up to 20080 share no factor with it.
- 4
The digits of 20080 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 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20080 = 2^{4} \times 5 \times 251 \]20080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 46872 |
| Euler totient φ(n) | 8000 |
| Square | 403206400 |
| Cube | 8096384512000 |
| Square root | 141.703917 (= 4√1255) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 92 |
| Scientific notation | 2.008 × |
20080 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand and eighty |
| Binary (base 2) | 100111001110000 |
| Octal (base 8) | 47160 |
| Hexadecimal (base 16) | 4E70 |
| Base 3 | 1000112201 |
| As time | 20080 seconds = 5 h 34 min 40 s |
Is 20080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20080 ÷ 2 = 10040) | 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 (20080 ÷ 4 = 5020) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20080 ÷ 5 = 4016) | 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 (20080 ÷ 8 = 2510) | 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 (20080 ÷ 10 = 2008) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20080 a prime number?
No. 20080 = × 5 × 251, so it is divisible by 2.
What are the factors of 20080?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 251, 502, 1004, 1255, 2008, 2510, 4016, 5020, 10040, 20080.
What is 20080 in binary?
100111001110000 (hexadecimal 4E70, octal 47160).
What is the square root of 20080?
About 141.7039, exactly 4√1255.
Is 20080 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 20080?
20080 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.