The number 331
331 is the 67th prime number. Its only divisors are 1 and 331.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 331: the 67th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
331 is prime, so its only factors are 1 and 331. It is the 67th prime; the next prime is 337 and the one before is 317.
- 3
The divisors add up to 332; without 331 itself that is 1, so 331 is deficient (1 is less than 331). Euler's totient φ(331) = 330 numbers up to 331 share no factor with it.
- 4
The digits of 331 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 24 steps to reach 1.
331 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 332 |
| Euler totient φ(n) | 330 |
| Square | 109561 |
| Cube | 36264691 |
| Square root | 18.193405 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 24 |
| Scientific notation | 3.31 × |
331 in other forms
| Form | Value |
|---|---|
| In words | three hundred and thirty-one |
| Roman numerals | CCCXXXI |
| Binary (base 2) | 101001011 |
| Octal (base 8) | 513 |
| Hexadecimal (base 16) | 14B |
| Base 3 | 110021 |
| As time | 331 seconds = 5 min 31 s |
Is 331 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 1) | 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 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 331 a prime number?
Yes. 331 is divisible only by 1 and itself.
What are the factors of 331?
1, 331.
What is 331 in binary?
101001011 (hexadecimal 14B, octal 513).
What is the square root of 331?
About 18.1934.
What is 331 in Roman numerals?
CCCXXXI.
Is 331 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 331?
331 is the 67th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.