To find the greatest common factor (GCF) of the terms [tex]\(6a^4\)[/tex] and [tex]\(4a^3\)[/tex], follow these steps:
1. Identify the coefficients:
- For [tex]\(6a^4\)[/tex], the coefficient is 6.
- For [tex]\(4a^3\)[/tex], the coefficient is 4.
2. Determine the greatest common factor of the coefficients:
- The factors of 6 are: 1, 2, 3, 6.
- The factors of 4 are: 1, 2, 4.
- The greatest common factor (GCF) of the numbers 6 and 4 is the highest number that divides both without a remainder. Here, the GCF is 2.
3. Identify the powers of the variable [tex]\(a\)[/tex]:
- For [tex]\(6a^4\)[/tex], the power of [tex]\(a\)[/tex] is 4.
- For [tex]\(4a^3\)[/tex], the power of [tex]\(a\)[/tex] is 3.
4. Determine the lowest power of the variable [tex]\(a\)[/tex]:
- The powers we have are 4 and 3.
- The lowest of these is 3.
5. Combine the GCF of the coefficients with the lowest power of the variable [tex]\(a\)[/tex]:
- The GCF of the coefficients is 2.
- The lowest power of [tex]\(a\)[/tex] is 3.
Therefore, the greatest common factor of [tex]\(6a^4\)[/tex] and [tex]\(4a^3\)[/tex] is [tex]\(2a^3\)[/tex].
