It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 557, the answer is: yes, 557 is a prime number because it has only two distinct divisors: 1 and itself (557).
As a consequence, 557 is only a multiple of 1 and 557..
Since 557 is a prime number, 557 is also a deficient number, that is to say 557 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 557 without 557 itself (that is 1, by definition!).
Parity of 557
557 is an odd number, because it is not evenly divisible by 2.
Is 557 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 557 is about 23.601.
Thus, the square root of 557 is not an integer, and therefore 557 is not a square number.
Anyway, 557 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 557?
The square of a number (here 557) is the result of the product of this number (557) by itself (i.e., 557 × 557); the square of 557 is sometimes called "raising 557 to the power 2", or "557 squared".
As a consequence, 557 is the square root of 310 249.
Number of digits of 557
557 is a number with 3 digits.
What are the multiples of 557?
The multiples of 557 are all integers evenly divisible by 557, that is all numbers such that the remainder of the division by 557 is zero. There are infinitely many multiples of 557. The smallest multiples of 557 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 557 too, since 0 × 557 = 0
- 557: indeed, 557 is a multiple of itself, since 557 is evenly divisible by 557 (we have 557 / 557 = 1, so the remainder of this division is indeed zero)
- 1 114: indeed, 1 114 = 557 × 2
- 1 671: indeed, 1 671 = 557 × 3
- 2 228: indeed, 2 228 = 557 × 4
- 2 785: indeed, 2 785 = 557 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 557). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 23.601). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.