The number 30013
30013 is a twin prime (30011 and 30013 are both prime) and the 3247th prime number. Its only divisors are 1 and 30013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 30013: a twin prime (30011 and 30013 are both prime); the 3247th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
30013 is prime, so its only factors are 1 and 30013. It is the 3247th prime; the next prime is 30029 and the one before is 30011.
- 3
The divisors add up to 30014; without 30013 itself that is 1, so 30013 is deficient (1 is less than 30013). Euler's totient φ(30013) = 30012 numbers up to 30013 share no factor with it.
- 4
The digits of 30013 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 64 steps to reach 1.
30013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 30014 |
| Euler totient φ(n) | 30012 |
| Square | 900780169 |
| Cube | 27035115212197 |
| Square root | 173.242604 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 64 |
| Scientific notation | 3.0013 × |
30013 in other forms
| Form | Value |
|---|---|
| In words | thirty thousand and thirteen |
| Binary (base 2) | 111010100111101 |
| Octal (base 8) | 72475 |
| Hexadecimal (base 16) | 753D |
| Base 3 | 1112011121 |
| As time | 30013 seconds = 8 h 20 min 13 s |
Is 30013 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 4) | 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 5) | 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 30013 a prime number?
Yes. 30013 is divisible only by 1 and itself.
What are the factors of 30013?
1, 30013.
What is 30013 in binary?
111010100111101 (hexadecimal 753D, octal 72475).
What is the square root of 30013?
About 173.2426.
Is 30013 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 30013?
30013 is a twin prime (30011 and 30013 are both prime); the 3247th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.