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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

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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
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Sep 30, 2012
Prime or Composite
by: Staff

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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
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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
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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 Number


Is 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).
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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
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