Prime Factorization
Prime factorization is a mathematical process that can be applied to find the most significant common factor (GCF) and least common multiple (LCM) of two or more numbers (Sowder, Sowder & Nickerson, 2012). The GCF is the most significant number that can be divided evenly into all given numbers. Contrastingly, the LCM is the smallest number that can be multiplied by each given number to produce the given numbers. A prime factorization process is valuable for finding the GCF and LCM of numbers. Need help with your assignment ? Reach out to us. We offer excellent services.
Using prime factorization, one can find the GCF by dividing all numbers by their prime factors. If the prime factors are all the same, the GCF is just that number.
For example:
The factors of 10 are 1, 2, 5, 10
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then, the most significant common factor is 10.
The LCM can be found by multiplying all numbers and finding the product of all prime factors (Sowder, Sowder & Nickerson, 2012).
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For Example:
Find the LCM of 14, 18, 24, 28, 32
LCM (14, 18, 24, 28, 32) = 2016
Steps:
Prime factorization of the numbers:
14 = 2 × 7
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
28 = 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
LCM=
= 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
= 2016
Prime factorization can be a valuable tool for finding the GCF and LCM of numbers, especially when large. It is an easy process that can be completed in minutes, resulting in two fundamental values that can be used to solve problems.
References
Sowder, J., Sowder, L., & Nickerson, S. (2012). Reconceptualizing mathematics. Macmillan Higher Education.
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Question 
Prime Factorization
In your own words, explain how prime factorization helps find the most significant common factor and least common multiple.