Is 230 a prime number? What are the divisors of 230?

Is 230 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 230, the answer is: No, 230 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 230) is as follows: 1, 2, 5, 10, 23, 46, 115, 230.

To be 230 a prime number, it would have been required that 230 has only two divisors, i.e., itself and 1.

As a consequence:

  • 230 is a multiple of 1
  • 230 is a multiple of 2
  • 230 is a multiple of 5
  • 230 is a multiple of 10
  • 230 is a multiple of 23
  • 230 is a multiple of 46
  • 230 is a multiple of 115

To be 230 a prime number, it would have been required that 230 has only two divisors, i.e., itself and 1.

Is 230 a deficient number?

Yes, 230 is a deficient number, that is to say 230 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 230 without 230 itself (that is 1 + 2 + 5 + 10 + 23 + 46 + 115 = 202).

Parity of 230

230 is an even number, because it is evenly divisible by 2: 230 / 2 = 115.

Is 230 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 230 is about 15.166.

Thus, the square root of 230 is not an integer, and therefore 230 is not a square number.

What is the square number of 230?

The square of a number (here 230) is the result of the product of this number (230) by itself (i.e., 230 × 230); the square of 230 is sometimes called "raising 230 to the power 2", or "230 squared".

The square of 230 is 52 900 because 230 × 230 = 2302 = 52 900.

As a consequence, 230 is the square root of 52 900.

Number of digits of 230

230 is a number with 3 digits.

What are the multiples of 230?

The multiples of 230 are all integers evenly divisible by 230, that is all numbers such that the remainder of the division by 230 is zero. There are infinitely many multiples of 230. The smallest multiples of 230 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 230 too, since 0 × 230 = 0
  • 230: indeed, 230 is a multiple of itself, since 230 is evenly divisible by 230 (we have 230 / 230 = 1, so the remainder of this division is indeed zero)
  • 460: indeed, 460 = 230 × 2
  • 690: indeed, 690 = 230 × 3
  • 920: indeed, 920 = 230 × 4
  • 1 150: indeed, 1 150 = 230 × 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 230). 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 15.166). 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 230

  • Preceding numbers: …228, 229
  • Following numbers: 231, 232

Nearest numbers from 230

  • Preceding prime number: 229
  • Following prime number: 233
Find out whether some integer is a prime number