Question

find the greatest common factor.
11, 12t², 8t³, 8
write your answer as a constant times a product of single variables raised to exponents.

Explanation:

Step1: Analyze constants

The constants are 11, 12, 8, 8. The factors of 11 are 1, 11; factors of 12 are 1, 2, 3, 4, 6, 12; factors of 8 are 1, 2, 4, 8. The greatest common factor of 11, 12, 8, 8 is 1.

Step2: Analyze variables

The terms with variables are \(12t^2\), \(8t^3\). The variable part is \(t\) with exponents 2 and 3. The lowest exponent of \(t\) is 0 (since 11 and 8 have no \(t\) term), so the variable part is \(t^0 = 1\).

Step3: Combine constant and variable

The GCF is the product of the GCF of constants and GCF of variables, which is \(1\times1 = 1\).

Answer:

1