The number 557
557 is the 102nd prime number. Its only divisors are 1 and 557.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 557: the 102nd prime number.
- 2
557 is prime, so its only factors are 1 and 557. It is the 102nd prime; the next prime is 563 and the one before is 547.
- 3
The divisors add up to 558; without 557 itself that is 1, so 557 is deficient (1 is less than 557). Euler's totient φ(557) = 556 numbers up to 557 share no factor with it.
- 4
The digits of 557 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
557 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 558 |
| Euler totient φ(n) | 556 |
| Square | 310249 |
| Cube | 172808693 |
| Square root | 23.600847 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 43 |
| Scientific notation | 5.57 × |
557 in other forms
| Form | Value |
|---|---|
| In words | five hundred and fifty-seven |
| Roman numerals | DLVII |
| Binary (base 2) | 1000101101 |
| Octal (base 8) | 1055 |
| Hexadecimal (base 16) | 22D |
| Base 3 | 202122 |
| As time | 557 seconds = 9 min 17 s |
Is 557 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 2) | 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 4) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 557 a prime number?
Yes. 557 is divisible only by 1 and itself.
What are the factors of 557?
1, 557.
What is 557 in binary?
1000101101 (hexadecimal 22D, octal 1055).
What is the square root of 557?
About 23.6008.
What is 557 in Roman numerals?
DLVII.
Is 557 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 557?
557 is the 102nd prime number.