91x2 y2z2, 21x5y6,105x4 what is the greatest common factor

Question

greatest common factor

Answer 1

Hi Diane, the greatest common factor represent what the largest coefficient and largest power that can be removed from each term.

 

Largest coefficient:

 

The three coefficients are 91, 21, 105

 

Factors of the three coefficients are:

 

91

---

 

1 * 91

7 * 13

 

21

---

 

1 * 21

7 * 3

 

105

----

 

1 * 105

3 * 35

5 * 21

7 * 15

 

What number do all three sets of factors have in common? Answer: 7. That means the largest common coefficient is 7. 

 

Largest power of x variable:

 

The x variable has powers of 2, 5, and 4. The largest power that can be removed from all three is 2. I cannot remove a power of 5 from all three terms and I cannot remove a power of 4 from all three terms.

 

Largest power of y variable:

 

The y variable has powers of 2, 6, and 0. The last term does not have a y variable, use a place holder of 0.

 

Because all three terms do not have a y variable, there is no power of the y variable common to all three terms.

 

Largest power of z variable:

 

The z variable is similar to the y variable because all three terms do not have a z variable.

 

The greatest common factor for all three terms is: 7x².

 

Questions?