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Answer :
To find the greatest common factor (GCF) of [tex]\(25x^2\)[/tex] and [tex]\(20x^3\)[/tex], follow these steps:
1. Find the GCF of the Coefficients:
Look at the coefficients of the terms, which are 25 and 20.
- The factors of 25 are 1, 5, and 25.
- The factors of 20 are 1, 2, 4, 5, 10, and 20.
The largest factor that both numbers share is 5. Thus, the GCF of 25 and 20 is 5.
2. Find the GCF of the Variables:
Consider the variable part, which are [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
- For the variable [tex]\(x\)[/tex], the GCF is determined by taking the smallest power of [tex]\(x\)[/tex] that appears in both terms. Here, that is [tex]\(x^2\)[/tex].
3. Combine the GCF of the Coefficients and the Variables:
The overall GCF of the terms [tex]\(25x^2\)[/tex] and [tex]\(20x^3\)[/tex] is the product of the GCF of the coefficients and the GCF of the variables.
Therefore, the GCF is:
[tex]\[
5 \times x^2 = 5x^2
\][/tex]
Thus, the greatest common factor of [tex]\(25x^2\)[/tex] and [tex]\(20x^3\)[/tex] is [tex]\(5x^2\)[/tex].
1. Find the GCF of the Coefficients:
Look at the coefficients of the terms, which are 25 and 20.
- The factors of 25 are 1, 5, and 25.
- The factors of 20 are 1, 2, 4, 5, 10, and 20.
The largest factor that both numbers share is 5. Thus, the GCF of 25 and 20 is 5.
2. Find the GCF of the Variables:
Consider the variable part, which are [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
- For the variable [tex]\(x\)[/tex], the GCF is determined by taking the smallest power of [tex]\(x\)[/tex] that appears in both terms. Here, that is [tex]\(x^2\)[/tex].
3. Combine the GCF of the Coefficients and the Variables:
The overall GCF of the terms [tex]\(25x^2\)[/tex] and [tex]\(20x^3\)[/tex] is the product of the GCF of the coefficients and the GCF of the variables.
Therefore, the GCF is:
[tex]\[
5 \times x^2 = 5x^2
\][/tex]
Thus, the greatest common factor of [tex]\(25x^2\)[/tex] and [tex]\(20x^3\)[/tex] is [tex]\(5x^2\)[/tex].
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