complete each factor tree do not use 1 as factor
Answers
One method for producing the prime factorization of a natural number is to use what is called a factor tree.
The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring. These two factors are the first branching in the factor tree. There are often several different pairs of factors that we could choose to begin the process. The choice does not matter; we may begin with any two factors. We repeat the process with each factor until each branch of the tree ends in a prime. Then the prime factorization is complete. The Fundamental Theorem of Arithmetictext annotation indicator guarantees that all prime factorizations of the same number will result in the same, unique prime factorization for the number.
Example: We show two of the ways of constructing a factor tree for 24.
Trees1.PNG
Continue factoring each tree until complete.
Trees2.PNG
Note that each tree ends with the unique prime factorization of 24 = 2 · 2 · 2 · 3 = 23 · 3.
There are two different styles for writing down the factor tree of a natural number. In the first style, as soon as we obtain a prime number in one of the branches, we circle it and then do not work on that branch any more. If a number at the end of a branch is still not prime (a composite), we find two factors for that value. Continue this process until the value at the end of each branch is a circled prime number. The prime factorization is the product of the circled primes.
Example:
Trees3.PNG
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