what is the greatest common factor using prime factoraztion for 90 and 126
ms.sue
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To find the greatest common factor (GCF) of 90 and 126 using prime factorization, we need to follow these steps:
Step 1: Prime Factorization of 90
To find the prime factorization of 90, we divide it by the smallest prime number, which is 2. Since 90 is an even number, we can divide it by 2:
90 ÷ 2 = 45
Now, we repeat the process with the quotient, which is 45:
45 ÷ 3 = 15
Finally, we divide 15 by 3, which gives us 5:
15 ÷ 5 = 3
Now, we have expressed 90 as a product of its prime factors: 2 × 3 × 3 × 5.
Step 2: Prime Factorization of 126
Similarly, we find the prime factorization of 126 by dividing it by 2:
126 ÷ 2 = 63
Next, we divide 63 by 3:
63 ÷ 3 = 21
Lastly, we divide 21 by 3:
21 ÷ 3 = 7
Therefore, the prime factorization of 126 is 2 × 3 × 3 × 7.
Step 3: Determine the Common Prime Factors
Now, we identify the common prime factors between 90 and 126. Looking at their prime factorizations, we see that both numbers share the factors of 2, 3, and 3.
Step 4: Find the GCF
To determine the GCF, we multiply the common prime factors together. In this case, the common prime factors are 2, 3, and 3:
GCF = 2 × 3 × 3 = 18
So, the greatest common factor (GCF) of 90 and 126 using prime factorization is 18.