557is an odd number,as it is not divisible by 2
The factors for 557 are all the numbers between -557 and 557 , which divide 557 without leaving any remainder. Since 557 divided by -557 is an integer, -557 is a factor of 557 .
Since 557 divided by -557 is a whole number, -557 is a factor of 557
Since 557 divided by -1 is a whole number, -1 is a factor of 557
Since 557 divided by 1 is a whole number, 1 is a factor of 557
Multiples of 557 are all integers divisible by 557 , i.e. the remainder of the full division by 557 is zero. There are infinite multiples of 557. The smallest multiples of 557 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 557 since 0 × 557 = 0
557 : in fact, 557 is a multiple of itself, since 557 is divisible by 557 (it was 557 / 557 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 557, the answer is: yes, 557 is a prime number because it only has two different divisors: 1 and itself (557).
To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 557). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 23.601 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.
More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.
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