The number 7013
7013 is the 902nd prime number. Its only divisors are 1 and 7013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7013: the 902nd prime number.
- 2
7013 is prime, so its only factors are 1 and 7013. It is the 902nd prime; the next prime is 7019 and the one before is 7001.
- 3
The divisors add up to 7014; without 7013 itself that is 1, so 7013 is deficient (1 is less than 7013). Euler's totient φ(7013) = 7012 numbers up to 7013 share no factor with it.
- 4
The digits of 7013 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 57 steps to reach 1.
7013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 7014 |
| Euler totient φ(n) | 7012 |
| Square | 49182169 |
| Cube | 344914551197 |
| Square root | 83.743656 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 57 |
| Scientific notation | 7.013 × |
7013 in other forms
| Form | Value |
|---|---|
| In words | seven thousand and thirteen |
| Binary (base 2) | 1101101100101 |
| Octal (base 8) | 15545 |
| Hexadecimal (base 16) | 1B65 |
| Base 3 | 100121202 |
| As time | 7013 seconds = 1 h 56 min 53 s |
Is 7013 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 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 2) | 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 7013 a prime number?
Yes. 7013 is divisible only by 1 and itself.
What are the factors of 7013?
1, 7013.
What is 7013 in binary?
1101101100101 (hexadecimal 1B65, octal 15545).
What is the square root of 7013?
About 83.7437.
Is 7013 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 7013?
7013 is the 902nd prime number.