# Algebra - Prime or Composite Number

by Shirley Tremble
(Brewton, AL, USA)

Prime or composite

• Define Prime Number

• Define Composite Number

How do you take a number such as 437 and determine if it is a prime or composite?

### Comments for Algebra - Prime or Composite Number

 Sep 30, 2012 Prime or Composite by: Staff Answer: Part I Define Prime Number       Prime number : any positive integer greater than one that can be divided by itself and the number one, without leaving a remainder (the number one, 1, is not a prime number) .       A prime number has only two factors: the number itself, and the number one.       No even number greater than the number 2 is a prime number.       However, not all odd numbers are prime numbers.       Any prime number which is greater than 2 is sometimes referred to as an “odd prime”.       The last digit of every prime number which is larger than 5 will always be 1, 3, 7, or 9.       For example, the following integers are prime numbers:                 2 = 1*2 are the only factors                 3 = 1*3 are the only factors                 5 = 1*5 are the only factors                 7 = 1*7 are the only factors                 11 = 1*11 are the only factors                 13 = 1*13 are the only factors                 17 = 1*17 are the only factors                 19 = 1*19 are the only factors                 23 = 1*23 are the only factors                 29 = 1*29 are the only factors                 31 = 1*31 are the only factors                 37 = 1*37 are the only factors                 41 = 1*41 are the only factors ----------------------------------------

 Sep 30, 2012 Prime or Composite by: Staff ---------------------------------------- Part II                 43 = 1*43 are the only factors                 47 = 1*47 are the only factors                 53 = 1*53 are the only factors                 59 = 1*59 are the only factors                 61 = 1*61 are the only factors                 67 = 1*67 are the only factors                 71 = 1*71 are the only factors                 73 = 1*73 are the only factors                 79 = 1*79 are the only factors                 83 = 1*83 are the only factors                 89 = 1*89 are the only factors                 97 = 1*97 are the only factors Define Composite Number       A Composite Number is a number that has three or more factors. These factors are the number “1”, and at least two more positive integers.       The following list shows both prime numbers and composite numbers:                 2 = 1*2 are the only factors → Prime Number                 3 = 1*3 are the only factors → Prime Number                 4 = 1*2*2 → Composite Number                 5 = 1*5 are the only factors → Prime Number                 6 = 1*2*3 → Composite Number ----------------------------------------

 Sep 30, 2012 Prime or Composite by: Staff ---------------------------------------- Part III                 7 = 1*7 are the only factors → Prime Number                 8 = 1*2*2*2 → Composite Number                 9 = 1*3*3 → Composite Number                 10 = 1*2*5 → Composite Number                 11 = 1*11 are the only factors → Prime Number                 12 = 1*2*2*3 → Composite Number                 13 = 1*13 are the only factors → Prime Number                 14 = 1*2*7 → Composite Number                 15 = 1*3*5 → Composite Number                 16 = 1*2*2*2*2 → Composite Number                 17 = 1*17 are the only factors → Prime Number                 18 = 1*2*3*3 → Composite Number                 19 = 1*19 are the only factors → Prime Number                 20 = 1*2*2*5 → Composite Number                 21 = 1*3*7 → Composite Number                 22 = 1*2*11 → Composite Number ----------------------------------------

 Sep 30, 2012 Prime or Composite by: Staff ----------------------------------------Part IV                23 = 1*23 are the only factors → Prime Number                24 = 1*2*2*2*3 → Composite Number                25 = 1*5*5 → Composite Number                 26 = 1*2*13 → Composite Number                27 = 1*3*3*3 → Composite Number                28 = 1*2*2*7 → Composite Number                29 = 1*29 are the only factors → Prime Number                30 = 1*2*3*5 → Composite NumberIs the number 437 a prime or a composite number?      The last digit of every prime number which is larger than 5 will always be 1, 3, 7, or 9.      On this basis, it is possible that the number 437 is a prime number. However, you cannot be certain.      There are several ways to find the answer to this question. However, I am only going to demonstrate the method called “Trial Division”.      Trial Division:                This method is time consuming.                Divide the number 437 by every positive integer, one at a time. If the divisor is a factor of 437, then the remainder will be zero (or the decimal will be zero). ----------------------------------------

 Sep 30, 2012 Prime or Composite by: Staff ---------------------------------------- Part V                 437 ÷ 2 = 218.5                 437 ÷ 3 = 145.667                 437 ÷ 4 = 109.25                 437 ÷ 5 = 87.4                 437 ÷ 6 = 72.8333                 437 ÷ 7 = 62.4286                 437 ÷ 8 = 54.625                 437 ÷ 9 = 48.5556                 437 ÷ 10 = 43.7                 437 ÷ 11 = 39.7273                 437 ÷ 12 = 36.4167                 437 ÷ 13 = 33.6154                 437 ÷ 14 = 31.2143                 437 ÷ 15 = 29.1333                 437 ÷ 16 = 27.3125                 437 ÷ 17 = 25.7059                 437 ÷ 18 = 24.2778                 437 ÷ 19 = 23; ∴19* 23 = 437→ 437 is a Composite Number Final Answer:                  437 is a Composite Number Thanks for writing. Staff www.solving-math-problems.com