Prime & Composite Numbers

The main difference between prime and composite numbers is the number of factors that they contain.

A prime number contains two factors, and one of those factors will always be 1. Essentially, a prime number is not divisible by any numbers other than 1.

Here is a list of some prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 71, 73, 79, 83, 89, 97, 101

Prime numbers can get very large; some can have thousands of digits. There are even different forms of prime numbers, such as Mersenne primes and primorial primes. Unless you are a mathematician, you really don't need to worry about them.

A composite number contains three (or more) factors. One of those factors again, is 1. The other numbers will be prime numbers. So a composite number is "composed" of prime numbers.

It helps to know some divisibility tricks when trying to determine what factors make up a composite number:

  • Even Numbers: Any even number is divisible by 2. If it is odd, then it is not divisible by 2.
  • Digital Roots: When you add up all the numbers of a digit, you get its digital root. If you get a multiple digit answer, then keep adding digits until you get a single digit. When you have a number with a digital root of 3, 6, or 9, it is divisible by 3. It only works for 3.
           Ex:  12345 = 1+2+3+4+5 = 15 = 1+5 = 6  ---> divisible by 3
                  455 = 4+5+5 = 14 = 1+4 = 5 ---> not divisible by 3
  •  Starting with a plus sign, alternate plus and minus signs in front of all digits and then solve them. If the answer is 0 or any number that is divisible by 11, then the number you solved for is divisible by 11.
           Ex: 781 = +7-8+1 = -1+1 = 0 ---> divisible by 11
                 616 = +6-1+6 = 5 + 6 = 11 ---> divisible by 11
                 820 = +8-2+0 = 6 ---> not divisible by 11
  • If a number ends in 5 or 0, it is divisible by 5.
Knowing some of these tricks can help you identify whether a number is prime or composite. For instance, if you see an even number, you can be fairly certain that it is divisible by 2.

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