Is 263 a prime number?

263 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 263 is about 16.217.

Thus, the square root of 263 is not an integer, and therefore 263 is not a square number.

Anyway, 263 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 263) is the result of the product of this number (263) by itself (i.e., 263 × 263); the square of 263 is sometimes called "raising 263 to the power 2", or "263 squared".

The square of 263 is 69 169 because 263 × 263 = 263² = 69 169.

As a consequence, 263 is the square root of 69 169.

263 is a number with 3 digits.

The multiples of 263 are all integers evenly divisible by 263, that is all numbers such that the remainder of the division by 263 is zero. There are infinitely many multiples of 263. The smallest multiples of 263 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 263 too, since 0 × 263 = 0
• 263: indeed, 263 is a multiple of itself, since 263 is evenly divisible by 263 (we have 263 / 263 = 1, so the remainder of this division is indeed zero)
• 526: indeed, 526 = 263 × 2
• 789: indeed, 789 = 263 × 3
• 1 052: indeed, 1 052 = 263 × 4
• 1 315: indeed, 1 315 = 263 × 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 263). 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 16.217). 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: …261, 262
• Following numbers: 264, 265…

Nearest numbers from 263

• Preceding prime number: 257
• Following prime number: 269

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• 263 est-il un nombre premier ?