The number 42013
42013 is the 4393rd prime number. Its only divisors are 1 and 42013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 42013: the 4393rd prime number.
- 2
42013 is prime, so its only factors are 1 and 42013. It is the 4393rd prime; the next prime is 42017 and the one before is 41999.
- 3
The divisors add up to 42014; without 42013 itself that is 1, so 42013 is deficient (1 is less than 42013). Euler's totient φ(42013) = 42012 numbers up to 42013 share no factor with it.
- 4
The digits of 42013 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 132 steps to reach 1.
42013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 42014 |
| Euler totient φ(n) | 42012 |
| Square | 1765092169 |
| Cube | 74156817296197 |
| Square root | 204.970730 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 132 |
| Scientific notation | 4.2013 × |
42013 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand and thirteen |
| Binary (base 2) | 1010010000011101 |
| Octal (base 8) | 122035 |
| Hexadecimal (base 16) | A41D |
| Base 3 | 2010122001 |
| As time | 42013 seconds = 11 h 40 min 13 s |
Is 42013 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 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 1) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42013 a prime number?
Yes. 42013 is divisible only by 1 and itself.
What are the factors of 42013?
1, 42013.
What is 42013 in binary?
1010010000011101 (hexadecimal A41D, octal 122035).
What is the square root of 42013?
About 204.9707.
Is 42013 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 42013?
42013 is the 4393rd prime number.