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Prime Factorization Chart

Prime factorization of a composite number is expressing the number as a product of prime numbers. The prime factorization is useful in determining the Greatest common factor and hence the Lowest common multiple of a number.There is only one prime factorization for any number as the order of factors does not matter. 

Methods of finding prime factorization

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There are two methods used to find the prime factorization of a number.
  1. Checking divisibility repeatedly
  2. Using a factor tree.
Indeed the method of using a factor tree is based on repeated divisions.  It shows the steps done in factoring as a tree.

What is a prime factorization chart?

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A prime factorization can be used like a table to find the prime factorization of a number falling in a range. Students can make such charts as an activity to display their understanding on the topic. Such charts can bring in the necessary math ambiance to the class room.

Prime factorization chart 1-100

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How to make a prime factorization chart for numbers 1 to 100?

It is good idea to list out the prime numbers in the list 1 to 100
Note 1 is neither a prime nor a composite number as it has only one factor that is itself.  The prime numbers from 1 to 100 are,
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83, 89 and 97.
In the table these numbers can be stated as prime.
The prime factorization for other numbers can be done from starting from the smallest composite number 4.
If a larger number has a smaller composite factors, the prime factors of the smaller can be used. It would not be necessary to find the prime factors of all composite numbers.
For example 8 = 2 x 4.  The prime factors of 4 = 2 x 2.  Hence the prime factorization of 8 = 2 x 2 x 2. The table can be thus completed till 100.

Number
Prime Factorization
Number
Prime Factorization
 1  Not composite  11  Prime
 2  Prime  12  2 x 2 x 3
 3  Prime  13  Prime
 4   2 x 2  14  2 x 7
 5  Prime  15  3 x 5
 6  2 x 3  16  2 x 2 x 2 x 2
 7  Prime  17 Prime
 8  2 x 2 x 2  18  2 x 3 x 3
 9  3 x 3             
 19  Prime
 10  2 x 5  20  2 x 2 x 5

Number
Prime Factorization
Number
Prime Factorization
 21  3 x 7  31  Prime
 22  2 x 11  32  2 x 2 x 2 x 2 x 2
 23  Prime  33  3 x 11
 24  2 x 2 x 2 x 3  34  2 x 17
 25  5 x 5  35  5 x 7
 26  2 x 13  36  2 x 2 x 3 x 3
 27  3 x 3 x 3  37  Prime
 28  2 x 2 x 7  38  2 x 19
 29  Prime  39  3 x 13
 30  2 x 3 x 5  40  2 x 2 x 2 x 5

Number
Prime Factorization
Number
Prime Factorization
 41  Prime  51  3 x 17
 42  2 x 3 x 7  52  2 x 2 x 13
 43  Prime  53  Prime
 44  2 x 2 x 11  54  2 x 3 x 3 x 3
 45  3 x 3 x 5  55  5 x 11
 46  2 x 23  56  2 x 2 x 2 x 7
 47  Prime  57  3 x 19
 48  2 x 2 x 2 x 2 x 3  58  2 x 29
 49  7 x 7  59  Prime
 50  2 x 5 x 5  60  2 x 2 x 3 x 5

Number
Prime Factorization
Number
Prime Factorization
 61  Prime  71  Prime
 62  2 x 31  72  2 x 2 x 2 x 3 x 3
 63  3 x 3 x 7  73  Prime
 64  2 x 2 x 2 x 2 x 2 x 2  74  2 x 37
 65  5 x 13  75  3 x 5 x 5
 66  2 x 3 x 11  76  2 x 2 x 19
 67  Prime  77  7 x 11
 68  2 x 2 x 17  78  2 x 3 x 13
 69  3 x 23  79  Prime
 70  2 x 5 x 7  80  2 x 2 x 2 x 2 x 5

Number
Prime Factorization
Number
Prime Factorization
 81  3 x 3 x 3 x 3
 91  7 x 13
 82  2 x 41  92  2 x 2 x 23
 83  Prime  93  3 x 31
 84  2 x 2 x 3 x 7  94  2 x 47
 85  5 x 17  95  5 x 19
 86  2 x 43  96  2 x 2 x 2 x 2 x 2 x 3
 87  3 x 29  97  Prime
 88  2 x 2 x 2 x 11  98  2 x 7 x 7
 89  Prime  99  3 x 3 x 11
 90  2 x 3 x 3 x 5  100  2 x 2 x 5 x 5

Prime Factorization Chart 1-1000

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A chart for the range 1-1000 can be made following the method shown for the range 1- 100.  First identify the prime numbers. Reuse the prime factorization of the smaller composite factors.10 sheets of chart can be made making in sheet a chart for 100 numbers.