The number 337
337 is the 68th prime number. Its only divisors are 1 and 337.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 337: the 68th prime number.
- 2
337 is prime, so its only factors are 1 and 337. It is the 68th prime; the next prime is 347 and the one before is 331.
- 3
The divisors add up to 338; without 337 itself that is 1, so 337 is deficient (1 is less than 337). Euler's totient φ(337) = 336 numbers up to 337 share no factor with it.
- 4
The digits of 337 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
337 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 338 |
| Euler totient φ(n) | 336 |
| Square | 113569 |
| Cube | 38272753 |
| Square root | 18.357560 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 112 |
| Scientific notation | 3.37 × |
337 in other forms
| Form | Value |
|---|---|
| In words | three hundred and thirty-seven |
| Roman numerals | CCCXXXVII |
| Binary (base 2) | 101010001 |
| Octal (base 8) | 521 |
| Hexadecimal (base 16) | 151 |
| Base 3 | 110111 |
| As time | 337 seconds = 5 min 37 s |
Is 337 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 2) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 337 a prime number?
Yes. 337 is divisible only by 1 and itself.
What are the factors of 337?
1, 337.
What is 337 in binary?
101010001 (hexadecimal 151, octal 521).
What is the square root of 337?
About 18.3576.
What is 337 in Roman numerals?
CCCXXXVII.
Is 337 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 337?
337 is the 68th prime number.