The number 8020
8020 is a composite number with 12 divisors. Its prime factorisation is × 5 × 401. Divisors (12): 1, 2, 4, 5, 10, 20, 401, 802, 1604, 2005, 4010, 8020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8020: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
8020 is composite. Its prime factorisation is
- 3
The divisors add up to 16884; without 8020 itself that is 8864, so 8020 is abundant (8864 is more than 8020). Euler's totient φ(8020) = 3200 numbers up to 8020 share no factor with it.
- 4
The digits of 8020 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 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8020 = 2^{2} \times 5 \times 401 \]8020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16884 |
| Euler totient φ(n) | 3200 |
| Square | 64320400 |
| Cube | 515849608000 |
| Square root | 89.554453 (= 2√2005) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 114 |
| Scientific notation | 8.02 × |
8020 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and twenty |
| Binary (base 2) | 1111101010100 |
| Octal (base 8) | 17524 |
| Hexadecimal (base 16) | 1F54 |
| Base 3 | 102000001 |
| As time | 8020 seconds = 2 h 13 min 40 s |
Is 8020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8020 ÷ 2 = 4010) | 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 (8020 ÷ 4 = 2005) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8020 ÷ 5 = 1604) | 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 5) | 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 | No (remainder 4) | 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 (8020 ÷ 10 = 802) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 8020 a prime number?
No. 8020 = × 5 × 401, so it is divisible by 2.
What are the factors of 8020?
1, 2, 4, 5, 10, 20, 401, 802, 1604, 2005, 4010, 8020.
What is 8020 in binary?
1111101010100 (hexadecimal 1F54, octal 17524).
What is the square root of 8020?
About 89.5545, exactly 2√2005.
Is 8020 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 8020?
8020 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.