The number 73013
73013 is the 7220th prime number. Its only divisors are 1 and 73013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73013: the 7220th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
73013 is prime, so its only factors are 1 and 73013. It is the 7220th prime; the next prime is 73019 and the one before is 73009.
- 3
The divisors add up to 73014; without 73013 itself that is 1, so 73013 is deficient (1 is less than 73013). Euler's totient φ(73013) = 73012 numbers up to 73013 share no factor with it.
- 4
The digits of 73013 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
73013 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 73014 |
| Euler totient φ(n) | 73012 |
| Square | 5330898169 |
| Cube | 389224868013197 |
| Square root | 270.209178 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.3013 × |
73013 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand and thirteen |
| Binary (base 2) | 10001110100110101 |
| Octal (base 8) | 216465 |
| Hexadecimal (base 16) | 11D35 |
| Base 3 | 10201011012 |
| As time | 73013 seconds = 20 h 16 min 53 s |
Is 73013 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 3) | 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 5) | 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 73013 a prime number?
Yes. 73013 is divisible only by 1 and itself.
What are the factors of 73013?
1, 73013.
What is 73013 in binary?
10001110100110101 (hexadecimal 11D35, octal 216465).
What is the square root of 73013?
About 270.2092.
Is 73013 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 73013?
73013 is the 7220th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.