Is 971 a prime number?

971 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 971 is about 31.161.

Thus, the square root of 971 is not an integer, and therefore 971 is not a square number.

Anyway, 971 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 971) is the result of the product of this number (971) by itself (i.e., 971 × 971); the square of 971 is sometimes called "raising 971 to the power 2", or "971 squared".

The square of 971 is 942 841 because 971 × 971 = 971² = 942 841.

As a consequence, 971 is the square root of 942 841.

971 is a number with 3 digits.

The multiples of 971 are all integers evenly divisible by 971, that is all numbers such that the remainder of the division by 971 is zero. There are infinitely many multiples of 971. The smallest multiples of 971 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 971 too, since 0 × 971 = 0
• 971: indeed, 971 is a multiple of itself, since 971 is evenly divisible by 971 (we have 971 / 971 = 1, so the remainder of this division is indeed zero)
• 1 942: indeed, 1 942 = 971 × 2
• 2 913: indeed, 2 913 = 971 × 3
• 3 884: indeed, 3 884 = 971 × 4
• 4 855: indeed, 4 855 = 971 × 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 971). 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 31.161). 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: …969, 970
• Following numbers: 972, 973…

Nearest numbers from 971

• Preceding prime number: 967
• Following prime number: 977

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• 971 est-il un nombre premier ?