What is the gcf of the terms 14c²d and 42c³d?

a. 2c²d
b. 7c²d
c. 3c
d. 14c²d

GCF - What is the highest number possible that the two given terms have in common.

In the given problem, one can clearly see that the two share .

The factors of 14 are 1, 2, 7 and 14 while the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Out of the two, 14 is the highest number that they both share.

So our answer will be 14

No you cannot.

Step-by-step explanation:

Let c be the amount of time it takes each machine to make 1 cockpit, and p be the amount of time it takes each machine to make 1 propulsion system.

For Machine A, we have 4 cockpits; this would take 4c time.  We also have 6 propulsion systems; this would take 6p time.  Together it takes 26 hours; this would give us

4c+6p=26.

For Machine B, we have 8 cockpits; this would take 8c time.  We also have 12 propulsion systems; this would take 12p time.  Together it takes 56 hours; this would give us

8c+12p=56

This gives us the system

To solve this, we want the coefficients of one of the variables to be the same.  To make the coefficients of c the same, we can multiply the top equation by 2:

To cancel c, we will subtract the second equation from the first one.  However, this also cancels p:

We get a statement that is not true; thus the system has no solution, and we cannot solve for a unique amount of time.

Hope this helps...