Question

Identify the greatest common factor of 15, a15a and 35, a, b35ab.

Answer 1

To identify the greatest common factor (GCF) of the terms 15, \( a^{15} \), and 35, \( a \), \( b^{35}ab \), we need to examine the numerical and variable parts of each expression.

1. **Numerical Components:**
- The numerical components are:
- 15 = \( 3 \times 5 \)
- 35 = \( 5 \times 7 \)
- The GCF of the numerical parts:
- The only common factor between 15 and 35 is 5.

2. **Variable Components:**
- The variable components of the expressions are:
- \( a^{15} \)
- \( a \)
- \( b^{35}ab = b^{35} \cdot a^1 \cdot b^1 = b^{36} \cdot a^1 \) (since \( b^{35}ab \) can be simplified to \( b^{35} \cdot a^1 \))

- For the variable \( a \):
- The minimum exponent of \( a \) from the terms is 1 (from \( a \)).
- For the variable \( b \):
- The term \( b^{36} \) does not appear in other factors, hence is not considered in the GCF.

3. **Combining Numerical and Variable Components:**
- The GCF of the numerical components is 5, and the GCF for the variable \( a \) is \( a^1 \), while \( b \) does not contribute as discussed above.

Putting it all together, the greatest common factor of the given terms 15, \( a^{15} \), 35, \( a \), \( b^{35}ab \) is:

\[
\text{GCF} = 5a
\]

So, the GCF is \( \boxed{5a} \).