The number 75013
75013 is a twin prime (75011 and 75013 are both prime) and the 7395th prime number. Its only divisors are 1 and 75013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 75013: a twin prime (75011 and 75013 are both prime); the 7395th prime number.
- 2
75013 is prime, so its only factors are 1 and 75013. It is the 7395th prime; the next prime is 75017 and the one before is 75011.
- 3
The divisors add up to 75014; without 75013 itself that is 1, so 75013 is deficient (1 is less than 75013). Euler's totient φ(75013) = 75012 numbers up to 75013 share no factor with it.
- 4
The digits of 75013 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
75013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 75014 |
| Euler totient φ(n) | 75012 |
| Square | 5626950169 |
| Cube | 422094413027197 |
| Square root | 273.885012 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.5013 × |
75013 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand and thirteen |
| Binary (base 2) | 10010010100000101 |
| Octal (base 8) | 222405 |
| Hexadecimal (base 16) | 12505 |
| Base 3 | 10210220021 |
| As time | 75013 seconds = 20 h 50 min 13 s |
Is 75013 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 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 7) | 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 75013 a prime number?
Yes. 75013 is divisible only by 1 and itself.
What are the factors of 75013?
1, 75013.
What is 75013 in binary?
10010010100000101 (hexadecimal 12505, octal 222405).
What is the square root of 75013?
About 273.8850.
Is 75013 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 75013?
75013 is a twin prime (75011 and 75013 are both prime); the 7395th prime number.