Is 317 a prime number? What are the divisors of 317?

## Parity of 317

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

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## Is 317 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 317 is about 17.804.

Thus, the square root of 317 is not an integer, and therefore 317 is not a square number.

Anyway, 317 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 317?

The square of a number (here 317) is the result of the product of this number (317) by itself (i.e., 317 × 317); the square of 317 is sometimes called "raising 317 to the power 2", or "317 squared".

The square of 317 is 100 489 because 317 × 317 = 3172 = 100 489.

As a consequence, 317 is the square root of 100 489.

## Number of digits of 317

317 is a number with 3 digits.

## What are the multiples of 317?

The multiples of 317 are all integers evenly divisible by 317, that is all numbers such that the remainder of the division by 317 is zero. There are infinitely many multiples of 317. The smallest multiples of 317 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 317). 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 17.804). 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 317

• Preceding numbers: …315, 316
• Following numbers: 318, 319

### Nearest numbers from 317

• Preceding prime number: 313
• Following prime number: 331
Find out whether some integer is a prime number