The number 5003
5003 is the 670th prime number. Its only divisors are 1 and 5003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5003: the 670th prime number.
- 2
5003 is prime, so its only factors are 1 and 5003. It is the 670th prime; the next prime is 5009 and the one before is 4999.
- 3
The divisors add up to 5004; without 5003 itself that is 1, so 5003 is deficient (1 is less than 5003). Euler's totient φ(5003) = 5002 numbers up to 5003 share no factor with it.
- 4
The digits of 5003 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 178 steps to reach 1.
5003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 5004 |
| Euler totient φ(n) | 5002 |
| Square | 25030009 |
| Cube | 125225135027 |
| Square root | 70.731888 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 178 |
| Scientific notation | 5.003 × |
5003 in other forms
| Form | Value |
|---|---|
| In words | five thousand and three |
| Binary (base 2) | 1001110001011 |
| Octal (base 8) | 11613 |
| Hexadecimal (base 16) | 138B |
| Base 3 | 20212022 |
| As time | 5003 seconds = 1 h 23 min 23 s |
Is 5003 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 5) | 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 8) | 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 9) | 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 5003 a prime number?
Yes. 5003 is divisible only by 1 and itself.
What are the factors of 5003?
1, 5003.
What is 5003 in binary?
1001110001011 (hexadecimal 138B, octal 11613).
What is the square root of 5003?
About 70.7319.
Is 5003 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 5003?
5003 is the 670th prime number.