Is 293 a prime number?

293 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 293 is about 17.117.

Thus, the square root of 293 is not an integer, and therefore 293 is not a square number.

Anyway, 293 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 293) is the result of the product of this number (293) by itself (i.e., 293 × 293); the square of 293 is sometimes called "raising 293 to the power 2", or "293 squared".

The square of 293 is 85 849 because 293 × 293 = 293² = 85 849.

As a consequence, 293 is the square root of 85 849.

293 is a number with 3 digits.

The multiples of 293 are all integers evenly divisible by 293, that is all numbers such that the remainder of the division by 293 is zero. There are infinitely many multiples of 293. The smallest multiples of 293 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 293 too, since 0 × 293 = 0
• 293: indeed, 293 is a multiple of itself, since 293 is evenly divisible by 293 (we have 293 / 293 = 1, so the remainder of this division is indeed zero)
• 586: indeed, 586 = 293 × 2
• 879: indeed, 879 = 293 × 3
• 1 172: indeed, 1 172 = 293 × 4
• 1 465: indeed, 1 465 = 293 × 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 293). 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 17.117). 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: …291, 292
• Following numbers: 294, 295…

Nearest numbers from 293

• Preceding prime number: 283
• Following prime number: 307

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• 293 est-il un nombre premier ?