Is 967 a prime number?

967 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 967 is about 31.097.

Thus, the square root of 967 is not an integer, and therefore 967 is not a square number.

Anyway, 967 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 967) is the result of the product of this number (967) by itself (i.e., 967 × 967); the square of 967 is sometimes called "raising 967 to the power 2", or "967 squared".

The square of 967 is 935 089 because 967 × 967 = 967² = 935 089.

As a consequence, 967 is the square root of 935 089.

967 is a number with 3 digits.

The multiples of 967 are all integers evenly divisible by 967, that is all numbers such that the remainder of the division by 967 is zero. There are infinitely many multiples of 967. The smallest multiples of 967 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 967 too, since 0 × 967 = 0
• 967: indeed, 967 is a multiple of itself, since 967 is evenly divisible by 967 (we have 967 / 967 = 1, so the remainder of this division is indeed zero)
• 1 934: indeed, 1 934 = 967 × 2
• 2 901: indeed, 2 901 = 967 × 3
• 3 868: indeed, 3 868 = 967 × 4
• 4 835: indeed, 4 835 = 967 × 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 967). 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 31.097). 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: …965, 966
• Following numbers: 968, 969…

Nearest numbers from 967

• Preceding prime number: 953
• Following prime number: 971

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• 967 est-il un nombre premier ?