Is 217 a prime number? What are the divisors of 217?

## Parity of 217

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

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## Is 217 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 217 is about 14.731.

Thus, the square root of 217 is not an integer, and therefore 217 is not a square number.

## What is the square number of 217?

The square of a number (here 217) is the result of the product of this number (217) by itself (i.e., 217 × 217); the square of 217 is sometimes called "raising 217 to the power 2", or "217 squared".

The square of 217 is 47 089 because 217 × 217 = 2172 = 47 089.

As a consequence, 217 is the square root of 47 089.

## Number of digits of 217

217 is a number with 3 digits.

## What are the multiples of 217?

The multiples of 217 are all integers evenly divisible by 217, that is all numbers such that the remainder of the division by 217 is zero. There are infinitely many multiples of 217. The smallest multiples of 217 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 217 too, since 0 × 217 = 0
• 217: indeed, 217 is a multiple of itself, since 217 is evenly divisible by 217 (we have 217 / 217 = 1, so the remainder of this division is indeed zero)
• 434: indeed, 434 = 217 × 2
• 651: indeed, 651 = 217 × 3
• 868: indeed, 868 = 217 × 4
• 1 085: indeed, 1 085 = 217 × 5
• etc.

## 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 217). 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 14.731). 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 217

• Preceding numbers: …215, 216
• Following numbers: 218, 219

### Nearest numbers from 217

• Preceding prime number: 211
• Following prime number: 223
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