It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 577, the answer is: yes, 577 is a prime number because it has only two distinct divisors: 1 and itself (577).
As a consequence, 577 is only a multiple of 1 and 577..
Since 577 is a prime number, 577 is also a deficient number, that is to say 577 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 577 without 577 itself (that is 1, by definition!).
Parity of 577
577 is an odd number, because it is not evenly divisible by 2.
Is 577 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 577 is about 24.021.
Thus, the square root of 577 is not an integer, and therefore 577 is not a square number.
Anyway, 577 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 577?
The square of a number (here 577) is the result of the product of this number (577) by itself (i.e., 577 × 577); the square of 577 is sometimes called "raising 577 to the power 2", or "577 squared".
As a consequence, 577 is the square root of 332 929.
Number of digits of 577
577 is a number with 3 digits.
What are the multiples of 577?
The multiples of 577 are all integers evenly divisible by 577, that is all numbers such that the remainder of the division by 577 is zero. There are infinitely many multiples of 577. The smallest multiples of 577 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 577 too, since 0 × 577 = 0
- 577: indeed, 577 is a multiple of itself, since 577 is evenly divisible by 577 (we have 577 / 577 = 1, so the remainder of this division is indeed zero)
- 1 154: indeed, 1 154 = 577 × 2
- 1 731: indeed, 1 731 = 577 × 3
- 2 308: indeed, 2 308 = 577 × 4
- 2 885: indeed, 2 885 = 577 × 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 577). 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 24.021). 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.