Is 853 a prime number?

853 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 853 is about 29.206.

Thus, the square root of 853 is not an integer, and therefore 853 is not a square number.

Anyway, 853 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 853) is the result of the product of this number (853) by itself (i.e., 853 × 853); the square of 853 is sometimes called "raising 853 to the power 2", or "853 squared".

The square of 853 is 727 609 because 853 × 853 = 853² = 727 609.

As a consequence, 853 is the square root of 727 609.

853 is a number with 3 digits.

The multiples of 853 are all integers evenly divisible by 853, that is all numbers such that the remainder of the division by 853 is zero. There are infinitely many multiples of 853. The smallest multiples of 853 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 853 too, since 0 × 853 = 0
• 853: indeed, 853 is a multiple of itself, since 853 is evenly divisible by 853 (we have 853 / 853 = 1, so the remainder of this division is indeed zero)
• 1 706: indeed, 1 706 = 853 × 2
• 2 559: indeed, 2 559 = 853 × 3
• 3 412: indeed, 3 412 = 853 × 4
• 4 265: indeed, 4 265 = 853 × 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 853). 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 29.206). 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: …851, 852
• Following numbers: 854, 855…

Nearest numbers from 853

• Preceding prime number: 839
• Following prime number: 857

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• 853 est-il un nombre premier ?