The number 1303
1303 is a twin prime (1301 and 1303 are both prime) and the 213th prime number. Its only divisors are 1 and 1303.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1303: a twin prime (1301 and 1303 are both prime); the 213th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1303 is prime, so its only factors are 1 and 1303. It is the 213th prime; the next prime is 1307 and the one before is 1301.
- 3
The divisors add up to 1304; without 1303 itself that is 1, so 1303 is deficient (1 is less than 1303). Euler's totient φ(1303) = 1302 numbers up to 1303 share no factor with it.
- 4
The digits of 1303 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 101 steps to reach 1.
1303 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1304 |
| Euler totient φ(n) | 1302 |
| Square | 1697809 |
| Cube | 2212245127 |
| Square root | 36.097091 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 101 |
| Scientific notation | 1.303 × |
1303 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and three |
| Roman numerals | MCCCIII |
| Binary (base 2) | 10100010111 |
| Octal (base 8) | 2427 |
| Hexadecimal (base 16) | 517 |
| Base 3 | 1210021 |
| As time | 1303 seconds = 21 min 43 s |
Is 1303 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 1) | 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 7) | 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 5) | 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 1303 a prime number?
Yes. 1303 is divisible only by 1 and itself.
What are the factors of 1303?
1, 1303.
What is 1303 in binary?
10100010111 (hexadecimal 517, octal 2427).
What is the square root of 1303?
About 36.0971.
What is 1303 in Roman numerals?
MCCCIII.
Is 1303 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1303?
1303 is a twin prime (1301 and 1303 are both prime); the 213th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.