The number 83003
83003 is the 8107th prime number. Its only divisors are 1 and 83003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83003: the 8107th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83003 is prime, so its only factors are 1 and 83003. It is the 8107th prime; the next prime is 83009 and the one before is 82997.
- 3
The divisors add up to 83004; without 83003 itself that is 1, so 83003 is deficient (1 is less than 83003). Euler's totient φ(83003) = 83002 numbers up to 83003 share no factor with it.
- 4
The digits of 83003 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 89 steps to reach 1.
83003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 83004 |
| Euler totient φ(n) | 83002 |
| Square | 6889498009 |
| Cube | 571849003241027 |
| Square root | 288.102412 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3003 × |
83003 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand and three |
| Binary (base 2) | 10100010000111011 |
| Octal (base 8) | 242073 |
| Hexadecimal (base 16) | 1443B |
| Base 3 | 11012212012 |
| As time | 83003 seconds = 23 h 3 min 23 s |
Is 83003 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 3) | 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 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 3) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83003 a prime number?
Yes. 83003 is divisible only by 1 and itself.
What are the factors of 83003?
1, 83003.
What is 83003 in binary?
10100010000111011 (hexadecimal 1443B, octal 242073).
What is the square root of 83003?
About 288.1024.
Is 83003 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 83003?
83003 is the 8107th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.