Find the GCF of the numbers using prime factorization.
84 and 126
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To find the greatest common factor (GCF) of two numbers using prime factorization, follow these steps:
Step 1: Prime factorize both numbers.
For 84:
84 can be written as the product of prime factors: 2 x 2 x 3 x 7.
For 126:
126 can be written as the product of prime factors: 2 x 3 x 3 x 7.
Step 2: Identify common prime factors.
Look for the common prime factors in both numbers, and take the smallest exponent for each shared factor. In this case, the common prime factors are 2, 3, and 7.
Step 3: Multiply the common prime factors.
To find the GCF, multiply the common prime factors identified in the previous step. In this case, the GCF is 2 x 3 x 7, which equals 42.
Therefore, the GCF of 84 and 126 is 42.