Is 214 a prime number? What are the divisors of 214?

## Parity of 214

214 is an even number, because it is evenly divisible by 2: 214 / 2 = 107.

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## Is 214 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 214 is about 14.629.

Thus, the square root of 214 is not an integer, and therefore 214 is not a square number.

## What is the square number of 214?

The square of a number (here 214) is the result of the product of this number (214) by itself (i.e., 214 × 214); the square of 214 is sometimes called "raising 214 to the power 2", or "214 squared".

The square of 214 is 45 796 because 214 × 214 = 2142 = 45 796.

As a consequence, 214 is the square root of 45 796.

## Number of digits of 214

214 is a number with 3 digits.

## What are the multiples of 214?

The multiples of 214 are all integers evenly divisible by 214, that is all numbers such that the remainder of the division by 214 is zero. There are infinitely many multiples of 214. The smallest multiples of 214 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 214 too, since 0 × 214 = 0
• 214: indeed, 214 is a multiple of itself, since 214 is evenly divisible by 214 (we have 214 / 214 = 1, so the remainder of this division is indeed zero)
• 428: indeed, 428 = 214 × 2
• 642: indeed, 642 = 214 × 3
• 856: indeed, 856 = 214 × 4
• 1 070: indeed, 1 070 = 214 × 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 214). 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 14.629). 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 214

• Preceding numbers: …212, 213
• Following numbers: 215, 216

### Nearest numbers from 214

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