To find the greatest common factor (GCF), I like to split it up into two steps:
1. Find the greatest common factor of the coefficients.
2. Find the greatest common factor of the variables and any exponents.
For starters, we will find the GCF of 14 and 18.
List the factors of 14:
1, 2, 7, 14
List the factors of 18:
1, 2, 3, 6, 9, 18
Now, find the factor that is the largest of the two: 2.
The GCF of 14 and 18 is 2.
Now, find the GCF of t² and t⁴.
Factors of t²: t, t²
Factors of t⁴: t, t², t⁴
The GCF of t² and t⁴ is t².
Now, put them together: 2t².
The GCF of 14t⁴ and 18t² is 2t².