The number 313
313 is a palindromic prime: it reads the same backwards and is prime, a twin prime (311 and 313 are both prime) and the 65th prime number. Its only divisors are 1 and 313.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 313: a palindromic prime: it reads the same backwards and is prime; a twin prime (311 and 313 are both prime); the 65th prime number; a palindrome: it reads 313 backwards too; a binary palindrome (100111001); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
313 is prime, so its only factors are 1 and 313. It is the 65th prime; the next prime is 317 and the one before is 311.
- 3
The divisors add up to 314; without 313 itself that is 1, so 313 is deficient (1 is less than 313). Euler's totient φ(313) = 312 numbers up to 313 share no factor with it.
- 4
The digits of 313 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 130 steps to reach 1.
313 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 314 |
| Euler totient φ(n) | 312 |
| Square | 97969 |
| Cube | 30664297 |
| Square root | 17.691806 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 130 |
| Scientific notation | 3.13 × |
313 in other forms
| Form | Value |
|---|---|
| In words | three hundred and thirteen |
| Roman numerals | CCCXIII |
| Binary (base 2) | 100111001 |
| Octal (base 8) | 471 |
| Hexadecimal (base 16) | 139 |
| Base 3 | 102121 |
| As time | 313 seconds = 5 min 13 s |
Is 313 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 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 1) | 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 1) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 313 a prime number?
Yes. 313 is divisible only by 1 and itself.
What are the factors of 313?
1, 313.
What is 313 in binary?
100111001 (hexadecimal 139, octal 471).
What is the square root of 313?
About 17.6918.
What is 313 in Roman numerals?
CCCXIII.
Is 313 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 313?
313 is a palindromic prime: it reads the same backwards and is prime; a twin prime (311 and 313 are both prime); the 65th prime number; a palindrome: it reads 313 backwards too; a binary palindrome (100111001); a happy number: repeatedly adding the squares of its digits reaches 1.