The greatest common factor of 70x^3, 110x^7 and 60x^8 is 10x.
The largest common factor (GCF) of a list of terms is the greatest number that is a factor of all of the terms. To find the GCF, we can use the following steps:
Prime factorize all of the terms.
Identify the prime factors that are common to all of the terms.
Multiply the common prime factors together.
Step 1: Prime factorize all of the terms.
70x3 = 2*5*7*x*x*x
110x7 = 2*5*11*x*x*x
60x8 = 2*2*3*5*x*x*x
Step 2: Identify the prime factors that are common to all of the terms.
The prime factors that are common to all of the terms are 2, 5, and x.
Step 3: Multiply the common prime factors together.
GCF = 2*5*x = 10x
Therefore, the largest common factor of the list of terms 70x3, 110x7, and 60x8 is 10x.
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Conclusion:
The largest common factor of the list of terms 70x3, 110x7, and 60x8 is 10x.