The number 343
343 is a perfect cube () and a palindrome: it reads 343 backwards too. Its prime factorisation is . Divisors (4): 1, 7, 49, 343.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 343: a perfect cube (); a palindrome: it reads 343 backwards too.
- 2
343 is composite. Its prime factorisation is
- 3
The divisors add up to 400; without 343 itself that is 57, so 343 is deficient (57 is less than 343). Euler's totient ฯ(343) = 294 numbers up to 343 share no factor with it.
- 4
The digits of 343 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 343 = 7^{3} \]343 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 400 |
| Euler totient ฯ(n) | 294 |
| Square | 117649 |
| Cube | 40353607 |
| Square root | 18.520259 (= 7โ7) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 125 |
| Scientific notation | 3.43 ร |
| Perfect power |
343 in other forms
| Form | Value |
|---|---|
| In words | three hundred and forty-three |
| Roman numerals | CCCXLIII |
| Binary (base 2) | 101010111 |
| Octal (base 8) | 527 |
| Hexadecimal (base 16) | 157 |
| Base 3 | 110201 |
| As time | 343 seconds = 5 min 43 s |
Is 343 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 | Yes (343 รท 7 = 49) | 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 1) | 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 2) | 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 343 a prime number?
No. 343 = , so it is divisible by 7.
What are the factors of 343?
1, 7, 49, 343.
What is 343 in binary?
101010111 (hexadecimal 157, octal 527).
What is the square root of 343?
About 18.5203, exactly 7โ7.
What is 343 in Roman numerals?
CCCXLIII.
Is 343 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 343?
343 is a perfect cube (); a palindrome: it reads 343 backwards too.