Answer :
To find the greatest common factor (GCF) of the expressions [tex]\(28x\)[/tex], [tex]\(70x^5\)[/tex], and [tex]\(14x^4\)[/tex], we need to look at both the numerical coefficients and the variable parts separately.
1. Numerical Coefficients:
- The coefficients of the expressions are 28, 70, and 14.
- To find the GCF of these numbers, we find the largest number that divides each of them without leaving a remainder.
- The factors of 28 are: 1, 2, 4, 7, 14, 28.
- The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70.
- The factors of 14 are: 1, 2, 7, 14.
- The common factors of 28, 70, and 14 are: 1, 2, 7, 14.
- The greatest of these common factors is 14.
2. Variable Parts:
- The variable parts are [tex]\(x\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x^4\)[/tex].
- We look for the lowest power of [tex]\(x\)[/tex] that appears in all expressions, which is [tex]\(x^1\)[/tex] (or just [tex]\(x\)[/tex]).
3. Combine the Results:
- The GCF of the coefficients is 14.
- The GCF of the variable parts is [tex]\(x\)[/tex].
- Therefore, the greatest common factor of the entire expressions is [tex]\(14x\)[/tex].
So, the greatest common factor of the expressions [tex]\(28x\)[/tex], [tex]\(70x^5\)[/tex], and [tex]\(14x^4\)[/tex] is [tex]\(14x\)[/tex].
1. Numerical Coefficients:
- The coefficients of the expressions are 28, 70, and 14.
- To find the GCF of these numbers, we find the largest number that divides each of them without leaving a remainder.
- The factors of 28 are: 1, 2, 4, 7, 14, 28.
- The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70.
- The factors of 14 are: 1, 2, 7, 14.
- The common factors of 28, 70, and 14 are: 1, 2, 7, 14.
- The greatest of these common factors is 14.
2. Variable Parts:
- The variable parts are [tex]\(x\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x^4\)[/tex].
- We look for the lowest power of [tex]\(x\)[/tex] that appears in all expressions, which is [tex]\(x^1\)[/tex] (or just [tex]\(x\)[/tex]).
3. Combine the Results:
- The GCF of the coefficients is 14.
- The GCF of the variable parts is [tex]\(x\)[/tex].
- Therefore, the greatest common factor of the entire expressions is [tex]\(14x\)[/tex].
So, the greatest common factor of the expressions [tex]\(28x\)[/tex], [tex]\(70x^5\)[/tex], and [tex]\(14x^4\)[/tex] is [tex]\(14x\)[/tex].
