Greatest Common Factor and Prime Factorization

Using Prime factorization to find HCF

by Yamileth Espinoza

​Highest Common Factor (HCF)

​The Highest Common Factor (HCF), also known as the Greatest Common Factor (GCF), of two (or more) numbers, is the largest number which is a factor of each.  In other words, it is the highest number that divides exactly into all of them

​Example: Find the HCF of 12 and 18

​Using the Listing method to find HCF we would list the factors of each number

​12: 1,2,3,4,6,12

​18: 1,2,3,6,9,18

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The common factors or of 12 and 18 are 1, 2, 3 and 6.

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The largest common factor is 6, so this is the H.C.F. of 12 and 18.

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​It is sometimes very easy to find a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4).

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However, if we have large numbers such as 36 and 54, it sometimes becomes tedious to list all their factors and then find the highest common factor.   Therefore, the method using prime factorization becomes very helpful in these cases.

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But how do you find the greatest common factor of two numbers using prime factorization?

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​Lets watch the following video

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Using prime factorization, ​Find the HCF of 18 and 45

​Using Prime Factorization to Find GCF

Find the HCF of 18, 24 and 30

Step 1: Use the factor tree to determine the prime factorization of numbers

​STEP 3: Circle the common factors

Multiple Choice

Which of the following shows the prime factorization of 32?

• $$2\times2\times2\times2\times2$$  

• $$2\times2\times2\times3\times2$$  

• $$2\times2\times3\times3\times2$$  

• $$2\times3\times3\times3\times2$$  

Multiple Choice

Which of the following shows the prime factorization of 48?

• $$1\times2\times2\times2\times2$$  

• $$2\times2\times2\times2\times3$$  

• $$2\times2\times2\times3\times3$$  

• $$2\times2\times3\times3\times3$$  

Multiple Choice

Looking at the image, what are the common prime factors of 32 and 48

• 2 and 3

• 2

• 2,2,2,2

• 2,2,3