The number 353
353 is a palindromic prime: it reads the same backwards and is prime, the 71st prime number and a palindrome: it reads 353 backwards too. Its only divisors are 1 and 353.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 353: a palindromic prime: it reads the same backwards and is prime; the 71st prime number; a palindrome: it reads 353 backwards too.
- 2
353 is prime, so its only factors are 1 and 353. It is the 71st prime; the next prime is 359 and the one before is 349.
- 3
The divisors add up to 354; without 353 itself that is 1, so 353 is deficient (1 is less than 353). Euler's totient φ(353) = 352 numbers up to 353 share no factor with it.
- 4
The digits of 353 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
353 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 354 |
| Euler totient φ(n) | 352 |
| Square | 124609 |
| Cube | 43986977 |
| Square root | 18.788294 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 125 |
| Scientific notation | 3.53 × |
353 in other forms
| Form | Value |
|---|---|
| In words | three hundred and fifty-three |
| Roman numerals | CCCLIII |
| Binary (base 2) | 101100001 |
| Octal (base 8) | 541 |
| Hexadecimal (base 16) | 161 |
| Base 3 | 111002 |
| As time | 353 seconds = 5 min 53 s |
Is 353 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 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 2) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 353 a prime number?
Yes. 353 is divisible only by 1 and itself.
What are the factors of 353?
1, 353.
What is 353 in binary?
101100001 (hexadecimal 161, octal 541).
What is the square root of 353?
About 18.7883.
What is 353 in Roman numerals?
CCCLIII.
Is 353 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 353?
353 is a palindromic prime: it reads the same backwards and is prime; the 71st prime number; a palindrome: it reads 353 backwards too.