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Answer :
The greatest common factor (GCF) of 70x^5, 110x^7, and 60x^8 is 10x^5.
To find the greatest common factor (GCF) for the list of terms 70x5, 110x7, and 60x8, we need to find the highest power and factor that is common to all terms. Let's break down each term into its prime factors:
70x5 = 2 * 5 * 7 * x * x * x * x * x
110x7 = 2 * 5 * 11 * x * x * x * x * x * x * x
60x8 = 2 * 2 * 3 * 5 * x * x * x * x * x * x * x * x
The GCF is the product of the common prime factors raised to the lowest powers they appear in all the terms. From the prime factorization, we can see that 2, 5, and x5 are common to all terms.
Therefore, the GCF is: 2 * 5 * x5 = 10x5.
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The Greatest Common Factor (GCF) of the terms 70x^(5), 110x^(7), and 60x^(8) is 10x^(5). The GCF is the highest number and the lowest power of x that can divide into all terms.
In mathematics, finding the Greatest Common Factor (GCF) means finding the largest number that can evenly divide into all of the numbers. To find the GCF of the terms 70x^(5), 110x^(7), and 60x^(8), we first find the GCF of the coefficients (numbers before the x) and then find the GCF of the variables (x terms).
The GCF of 70, 110, and 60 is 10. For the x terms, we take the lowest exponent. In this case, x^(5) is the smallest exponent.
So, the GCF of 70x^(5), 110x^(7), and 60x^(8) is 10x^(5).
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