The number 40013
40013 is the 4205th prime number. Its only divisors are 1 and 40013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40013: the 4205th prime number.
- 2
40013 is prime, so its only factors are 1 and 40013. It is the 4205th prime; the next prime is 40031 and the one before is 40009.
- 3
The divisors add up to 40014; without 40013 itself that is 1, so 40013 is deficient (1 is less than 40013). Euler's totient φ(40013) = 40012 numbers up to 40013 share no factor with it.
- 4
The digits of 40013 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 67 steps to reach 1.
40013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 40014 |
| Euler totient φ(n) | 40012 |
| Square | 1601040169 |
| Cube | 64062420282197 |
| Square root | 200.032497 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 67 |
| Scientific notation | 4.0013 × |
40013 in other forms
| Form | Value |
|---|---|
| In words | forty thousand and thirteen |
| Binary (base 2) | 1001110001001101 |
| Octal (base 8) | 116115 |
| Hexadecimal (base 16) | 9C4D |
| Base 3 | 2000212222 |
| As time | 40013 seconds = 11 h 6 min 53 s |
Is 40013 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 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 6) | 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 40013 a prime number?
Yes. 40013 is divisible only by 1 and itself.
What are the factors of 40013?
1, 40013.
What is 40013 in binary?
1001110001001101 (hexadecimal 9C4D, octal 116115).
What is the square root of 40013?
About 200.0325.
Is 40013 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 40013?
40013 is the 4205th prime number.