# 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

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?

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

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

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.