To find an expression that is a factor of the terms 3ab, 6a, 4b, and 8, we need to determine the greatest common factor (GCF) of these terms. Let’s analyze each term:
- 3ab has factors of 3, a, and b.
- 6a has factors of 6 and a.
- 4b has factors of 4 and b.
- 8 has factors of 8.
Next, we need to find numeric and variable common factors:
Step 1: Find the numeric GCF
The numeric factors are:
- 3 from 3ab
- 6 from 6a
- 4 from 4b
- 8 from 8
The GCF of these numbers is 1, as there are no other common numeric factors greater than 1.
Step 2: Find the variable GCF
Now, let’s look at the variables:
- 3ab contains both a and b.
- 6a contains a.
- 4b contains b.
- 8 contains no variables.
The only variable that appears in more than one term is a (in 3ab and 6a), and b appears in 3ab and 4b.
Conclusion
Thus, the GCF considering both numbers and variables is:
- Numeric: 1
- Variables: None that are common to all terms.
As there are no common factors greater than 1 across all terms, we can conclude that 1 is the only factor common to 3ab, 6a, 4b, and 8. Therefore, the answer is simply:
1 – indicating that no higher common factor exists among these expressions.