The number 80200
80200 is a triangular number: 1 + 2 + … + 400 = 80200. Its prime factorisation is × × 401. Divisors (24): 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 401, 802, 1604, 2005 … 80200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 80200: a triangular number: 1 + 2 + … + 400 = 80200; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
80200 is composite. Its prime factorisation is
- 3
The divisors add up to 186930; without 80200 itself that is 106730, so 80200 is abundant (106730 is more than 80200). Euler's totient φ(80200) = 32000 numbers up to 80200 share no factor with it.
- 4
The digits of 80200 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 80200 = 2^{3} \times 5^{2} \times 401 \]80200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 186930 |
| Euler totient φ(n) | 32000 |
| Square | 6432040000 |
| Cube | 515849608000000 |
| Square root | 283.196045 (= 10√802) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 94 |
| Scientific notation | 8.02 × |
80200 in other forms
| Form | Value |
|---|---|
| In words | eighty thousand two hundred |
| Binary (base 2) | 10011100101001000 |
| Octal (base 8) | 234510 |
| Hexadecimal (base 16) | 13948 |
| Base 3 | 11002000101 |
| As time | 80200 seconds = 22 h 16 min 40 s |
Is 80200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (80200 ÷ 2 = 40100) | 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 (80200 ÷ 4 = 20050) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (80200 ÷ 5 = 16040) | 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 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 (80200 ÷ 8 = 10025) | 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 (80200 ÷ 10 = 8020) | 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 80200 a prime number?
No. 80200 = × × 401, so it is divisible by 2.
What are the factors of 80200?
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 401, 802, 1604, 2005, 3208, 4010, 8020, 10025, 16040, 20050, 40100, 80200.
What is 80200 in binary?
10011100101001000 (hexadecimal 13948, octal 234510).
What is the square root of 80200?
About 283.1960, exactly 10√802.
Is 80200 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 80200?
80200 is a triangular number: 1 + 2 + … + 400 = 80200; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.