Is 231 a prime number? What are the divisors of 231?

Parity of 231

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

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Is 231 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 231 is about 15.199.

Thus, the square root of 231 is not an integer, and therefore 231 is not a square number.

What is the square number of 231?

The square of a number (here 231) is the result of the product of this number (231) by itself (i.e., 231 × 231); the square of 231 is sometimes called "raising 231 to the power 2", or "231 squared".

The square of 231 is 53 361 because 231 × 231 = 2312 = 53 361.

As a consequence, 231 is the square root of 53 361.

Number of digits of 231

231 is a number with 3 digits.

What are the multiples of 231?

The multiples of 231 are all integers evenly divisible by 231, that is all numbers such that the remainder of the division by 231 is zero. There are infinitely many multiples of 231. The smallest multiples of 231 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 231 too, since 0 × 231 = 0
  • 231: indeed, 231 is a multiple of itself, since 231 is evenly divisible by 231 (we have 231 / 231 = 1, so the remainder of this division is indeed zero)
  • 462: indeed, 462 = 231 × 2
  • 693: indeed, 693 = 231 × 3
  • 924: indeed, 924 = 231 × 4
  • 1 155: indeed, 1 155 = 231 × 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 231). 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 15.199). 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 231

  • Preceding numbers: …229, 230
  • Following numbers: 232, 233…

Nearest numbers from 231

  • Preceding prime number: 229
  • Following prime number: 233
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