Finding GCF of 3 Terms: 102k^5m^2, 51k^4m, 153k^2m^2

[dizco29]

hey guys, getting back into some basic algebra (so hope you don't mind a real newbie) and was doing a factoring tutorial on the web, and came across this.

The work for finding the GCF of three terms is shown below.

102k^5m^2
51k^4m
153k^2m^2


First find the GCF of the coefficients:
102 (1, 2, 3, 6, 17, 34, 51, 102)
51 (1, 3, 17, 51)
153 (1, 3, 9, 17, 51, 153)
GCF (of coefficients only) = 51


Next find the GCF of the variables:

k^5 m^2

k^4 m

k^2 m^2

GCF (of variables) = k2m


Now multiply the two GCFs
GCF of the entire term = 51k^2 m

what I don't understand is how the GCF for K is 2. Because 5 is not divisble by 2. So how can that be?

here's a link to the page if the above is not clear.

http://www.algebrahelp.com/lessons/f...indgcf/pg2.htm

Thanks!

 

[neutrino]

k^5 = k x k x k x k x k = k^2 x k^3. Does that help?

 

[dizco29]

hmmm, kinda, can you explain a little bit more about it. didn't know that you can add the exponents when you are looking for the GCF

 

[neutrino]

Let us denote k^2 by n. Therefore k^5 = n.k^3 and k^2 = n. Therefore n is the GCF.

 

[dizco29]

I think I understand your explanation for the my first question. how about in this case.


Simplifying
z^3 + 4z^2

Reorder the terms:
4z^2 + z^3

Factor out the Greatest Common Factor (GCF), 'z^2'.
z^2(4 + z)Final result:z^2(4 + z)



I still don't get how in this case the common factor for z is ^2. shouldn't it be z^1?


you can check it out here:

http://www.algebrahelp.com/calculators/expression/factoring/calc.do?expression=z^3+++4z^2


thanks!

 

[dizco29]

cool, I get it now! stupid me lol. thanks for your explainantion!

 

[neutrino]

I still don't get how in this case the common factor for z is ^2. shouldn't it be z^1?
thanks!

z^3 = z^2 x z

 

[neutrino]

cool, I get it now! stupid me lol. thanks for your explainantion!

You're welcome.

 

[HallsofIvy]

what I don't understand is how the GCF for K is 2. Because 5 is not divisble by 2. So how can that be?

You're error is clear in the wording- "The GCF for K" is not 2! It is k². 5 is not divisible by 2 but k⁵ certainly is divisible by k².

 

[mathwonk]

this is a slly problem to do by that method. this poroblem involves only the same prime factors. e.g. to find the gcf of expressions of form a^n b^m c^p, where a,b,c, are all prime, just take each prime and raise it to the smallest power it has in any term given.

e,g, in your example you have 3^r 17^s k^t m^u, and just taking the smallest power of each occurrence gives immediately 3^1 17^1 k^2 m^1.