Is 997 a prime number? What are the divisors of 997?

## Parity of 997

997 is an odd number, because it is not evenly divisible by 2.

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## Is 997 a perfect square 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 997 is about 31.575.

Thus, the square root of 997 is not an integer, and therefore 997 is not a square number.

Anyway, 997 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 997?

The square of a number (here 997) is the result of the product of this number (997) by itself (i.e., 997 × 997); the square of 997 is sometimes called "raising 997 to the power 2", or "997 squared".

The square of 997 is 994 009 because 997 × 997 = 9972 = 994 009.

As a consequence, 997 is the square root of 994 009.

## Number of digits of 997

997 is a number with 3 digits.

## What are the multiples of 997?

The multiples of 997 are all integers evenly divisible by 997, that is all numbers such that the remainder of the division by 997 is zero. There are infinitely many multiples of 997. The smallest multiples of 997 are:

## How to determine whether an integer is a prime number?

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 997). 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 31.575). 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.

## Numbers near 997

• Preceding numbers: …995, 996
• Following numbers: 998, 999

### Nearest numbers from 997

• Preceding prime number: 991
• Following prime number: 1 009
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