The number 22003
22003 is the 2465th prime number. Its only divisors are 1 and 22003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 22003: the 2465th prime number.
- 2
22003 is prime, so its only factors are 1 and 22003. It is the 2465th prime; the next prime is 22013 and the one before is 21997.
- 3
The divisors add up to 22004; without 22003 itself that is 1, so 22003 is deficient (1 is less than 22003). Euler's totient φ(22003) = 22002 numbers up to 22003 share no factor with it.
- 4
The digits of 22003 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 69 steps to reach 1.
22003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 22004 |
| Euler totient φ(n) | 22002 |
| Square | 484132009 |
| Cube | 10652356594027 |
| Square root | 148.334082 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.2003 × |
22003 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand and three |
| Binary (base 2) | 101010111110011 |
| Octal (base 8) | 52763 |
| Hexadecimal (base 16) | 55F3 |
| Base 3 | 1010011221 |
| As time | 22003 seconds = 6 h 6 min 43 s |
Is 22003 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 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 22003 a prime number?
Yes. 22003 is divisible only by 1 and itself.
What are the factors of 22003?
1, 22003.
What is 22003 in binary?
101010111110011 (hexadecimal 55F3, octal 52763).
What is the square root of 22003?
About 148.3341.
Is 22003 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 22003?
22003 is the 2465th prime number.