The number 82013
82013 is the 8021st prime number. Its only divisors are 1 and 82013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 82013: the 8021st prime number.
- 2
82013 is prime, so its only factors are 1 and 82013. It is the 8021st prime; the next prime is 82021 and the one before is 82009.
- 3
The divisors add up to 82014; without 82013 itself that is 1, so 82013 is deficient (1 is less than 82013). Euler's totient φ(82013) = 82012 numbers up to 82013 share no factor with it.
- 4
The digits of 82013 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
82013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 82014 |
| Euler totient φ(n) | 82012 |
| Square | 6726132169 |
| Cube | 551630277576197 |
| Square root | 286.379119 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.2013 × |
82013 in other forms
| Form | Value |
|---|---|
| In words | eighty-two thousand and thirteen |
| Binary (base 2) | 10100000001011101 |
| Octal (base 8) | 240135 |
| Hexadecimal (base 16) | 1405D |
| Base 3 | 11011111112 |
| As time | 82013 seconds = 22 h 46 min 53 s |
Is 82013 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 82013 a prime number?
Yes. 82013 is divisible only by 1 and itself.
What are the factors of 82013?
1, 82013.
What is 82013 in binary?
10100000001011101 (hexadecimal 1405D, octal 240135).
What is the square root of 82013?
About 286.3791.
Is 82013 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 82013?
82013 is the 8021st prime number.