Example of how to identify prime and composite numbers

Mathematics differentiates between two types of numbers: prime and composite. In this sense the prime numbers would be those that have only two dividers, that is, they can only be divided between the number 1 and between themselves. While compound numbers are those that can be divided by more than two dividers.


In this sense we have that the prime numbers would be as follows: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 27, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, etc. A quick way to check if we are in the presence of a prime number is to try to split it, to check the number of dividers you can have. For example:

Let’s consider the number 41, and try to check how many dividers this number can have.


  • If we divide 41 by 2, the result will be 20.5
  • If we divide 41 by 3, the result will be 13.6
  • If we divide 41 by 10, the result will be 4.1
  • If we divide 41 by 20, the result will be 2.5

Obtaining that none of the proposed dividers yield full numbers. Now if we deal with the number 1 and the same 41, we get the following:

  • If we divide 41 by 1, the result will be 41
  • If we divide 41 by 41, the result will be 1

That is, the number 41 only yields full numbers when it is divided between the unit (1) and between it, having only two dividers. When this happens we are in the presence of a Prime Number.

For its part, the compound numbers would be: 4, 6, 8, 9, 10, 12, 14,, 15, 16, 18, 20, 21, 22, 24, 25, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, etc. As with prime numbers, a practical way to check if we are in the presence of a compound number is to take the number in question and divide it, in order to check how many dividers you have. For example:

Let’s consider the number 30, and proceed to divide it by the following numbers:

  • If we divide 30 by 1, the result will be 30
  • If we divide 30 by 2, the result will be 15
  • If we divide 30 by 3, the result will be 10
  • If we divide 30 by 5, the result will be 6
  • If we divide 30 by 6, the result will be 5
  • If we divide 30 by 30, the result will be 1

That is, the number 30 has more than two dividers, which divides it into full numbers. Therefore we are in the presence of a Composite Number.

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Example of how to identify prime and composite numbers
Source: Education  
August 22, 2019


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