Is 577 a prime number?

577 is an odd number, because it is not evenly divisible by 2.

Find out more:

• What is an even 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.

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".

The square of 577 is 332 929 because 577 × 577 = 577² = 332 929.

As a consequence, 577 is the square root of 332 929.

577 is a number with 3 digits.

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
• etc.

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.

• Preceding numbers: …575, 576
• Following numbers: 578, 579…

Nearest numbers from 577

• Preceding prime number: 571
• Following prime number: 587

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• 577 est-il un nombre premier ?