The number 4013
4013 is the 554th prime number. Its only divisors are 1 and 4013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4013: the 554th prime number.
- 2
4013 is prime, so its only factors are 1 and 4013. It is the 554th prime; the next prime is 4019 and the one before is 4007.
- 3
The divisors add up to 4014; without 4013 itself that is 1, so 4013 is deficient (1 is less than 4013). Euler's totient φ(4013) = 4012 numbers up to 4013 share no factor with it.
- 4
The digits of 4013 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
4013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 4014 |
| Euler totient φ(n) | 4012 |
| Square | 16104169 |
| Cube | 64626030197 |
| Square root | 63.348244 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 43 |
| Scientific notation | 4.013 × |
4013 in other forms
| Form | Value |
|---|---|
| In words | four thousand and thirteen |
| Binary (base 2) | 111110101101 |
| Octal (base 8) | 7655 |
| Hexadecimal (base 16) | FAD |
| Base 3 | 12111122 |
| As time | 4013 seconds = 1 h 6 min 53 s |
Is 4013 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 2) | 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 8) | 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 9) | 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 4013 a prime number?
Yes. 4013 is divisible only by 1 and itself.
What are the factors of 4013?
1, 4013.
What is 4013 in binary?
111110101101 (hexadecimal FAD, octal 7655).
What is the square root of 4013?
About 63.3482.
Is 4013 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 4013?
4013 is the 554th prime number.