Is 189 a prime number? What are the divisors of 189?

Parity of 189

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

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Is 189 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 189 is about 13.748.

Thus, the square root of 189 is not an integer, and therefore 189 is not a square number.

What is the square number of 189?

The square of a number (here 189) is the result of the product of this number (189) by itself (i.e., 189 × 189); the square of 189 is sometimes called "raising 189 to the power 2", or "189 squared".

The square of 189 is 35 721 because 189 × 189 = 1892 = 35 721.

As a consequence, 189 is the square root of 35 721.

Number of digits of 189

189 is a number with 3 digits.

What are the multiples of 189?

The multiples of 189 are all integers evenly divisible by 189, that is all numbers such that the remainder of the division by 189 is zero. There are infinitely many multiples of 189. The smallest multiples of 189 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 189 too, since 0 × 189 = 0
  • 189: indeed, 189 is a multiple of itself, since 189 is evenly divisible by 189 (we have 189 / 189 = 1, so the remainder of this division is indeed zero)
  • 378: indeed, 378 = 189 × 2
  • 567: indeed, 567 = 189 × 3
  • 756: indeed, 756 = 189 × 4
  • 945: indeed, 945 = 189 × 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 189). 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 13.748). 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 189

  • Preceding numbers: …187, 188
  • Following numbers: 190, 191…

Nearest numbers from 189

  • Preceding prime number: 181
  • Following prime number: 191
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