Is 164 a prime number? What are the divisors of 164?

## Parity of 164

164 is an even number, because it is evenly divisible by 2: 164 / 2 = 82.

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## Is 164 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 164 is about 12.806.

Thus, the square root of 164 is not an integer, and therefore 164 is not a square number.

## What is the square number of 164?

The square of a number (here 164) is the result of the product of this number (164) by itself (i.e., 164 × 164); the square of 164 is sometimes called "raising 164 to the power 2", or "164 squared".

The square of 164 is 26 896 because 164 × 164 = 1642 = 26 896.

As a consequence, 164 is the square root of 26 896.

## Number of digits of 164

164 is a number with 3 digits.

## What are the multiples of 164?

The multiples of 164 are all integers evenly divisible by 164, that is all numbers such that the remainder of the division by 164 is zero. There are infinitely many multiples of 164. The smallest multiples of 164 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 164 too, since 0 × 164 = 0
• 164: indeed, 164 is a multiple of itself, since 164 is evenly divisible by 164 (we have 164 / 164 = 1, so the remainder of this division is indeed zero)
• 328: indeed, 328 = 164 × 2
• 492: indeed, 492 = 164 × 3
• 656: indeed, 656 = 164 × 4
• 820: indeed, 820 = 164 × 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 164). 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 12.806). 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 164

• Preceding numbers: …162, 163
• Following numbers: 165, 166

### Nearest numbers from 164

• Preceding prime number: 163
• Following prime number: 167
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