Is 313 a prime number?

313 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 313 is about 17.692.

Thus, the square root of 313 is not an integer, and therefore 313 is not a square number.

Anyway, 313 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 313) is the result of the product of this number (313) by itself (i.e., 313 × 313); the square of 313 is sometimes called "raising 313 to the power 2", or "313 squared".

The square of 313 is 97 969 because 313 × 313 = 313² = 97 969.

As a consequence, 313 is the square root of 97 969.

313 is a number with 3 digits.

The multiples of 313 are all integers evenly divisible by 313, that is all numbers such that the remainder of the division by 313 is zero. There are infinitely many multiples of 313. The smallest multiples of 313 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 313 too, since 0 × 313 = 0
• 313: indeed, 313 is a multiple of itself, since 313 is evenly divisible by 313 (we have 313 / 313 = 1, so the remainder of this division is indeed zero)
• 626: indeed, 626 = 313 × 2
• 939: indeed, 939 = 313 × 3
• 1 252: indeed, 1 252 = 313 × 4
• 1 565: indeed, 1 565 = 313 × 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 313). 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 17.692). 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: …311, 312
• Following numbers: 314, 315…

Nearest numbers from 313

• Preceding prime number: 311
• Following prime number: 317

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• 313 est-il un nombre premier ?