Is 857 a prime number?

857 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 857 is about 29.275.

Thus, the square root of 857 is not an integer, and therefore 857 is not a square number.

Anyway, 857 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 857) is the result of the product of this number (857) by itself (i.e., 857 × 857); the square of 857 is sometimes called "raising 857 to the power 2", or "857 squared".

The square of 857 is 734 449 because 857 × 857 = 857² = 734 449.

As a consequence, 857 is the square root of 734 449.

857 is a number with 3 digits.

The multiples of 857 are all integers evenly divisible by 857, that is all numbers such that the remainder of the division by 857 is zero. There are infinitely many multiples of 857. The smallest multiples of 857 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 857 too, since 0 × 857 = 0
• 857: indeed, 857 is a multiple of itself, since 857 is evenly divisible by 857 (we have 857 / 857 = 1, so the remainder of this division is indeed zero)
• 1 714: indeed, 1 714 = 857 × 2
• 2 571: indeed, 2 571 = 857 × 3
• 3 428: indeed, 3 428 = 857 × 4
• 4 285: indeed, 4 285 = 857 × 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 857). 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 29.275). 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: …855, 856
• Following numbers: 858, 859…

Nearest numbers from 857

• Preceding prime number: 853
• Following prime number: 859

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• 857 est-il un nombre premier ?