GCF Of 2 Monomials

I fail to understand why I am being told by Aleks that the greatest common factor of 15y^3 and 13c^4 is 1.

It seems it should be:
GCF of 13 and 15 = 1
y^3 and c^4 are different terms, therefore it would seem incorrect to say they have a common factor of 1 (like Aleks says it is). So the greatest common factors I would have thought would be:

1*y^3*c^4

What am I missing.

You're mostly correct in your reasoning except for one thing - any two terms will always share a common factor of 1. You can think of the "GCF" as a function which takes 2 (or more) terms as arguments. Then, given n terms, this pseudocode is what the function does:

Look at the first term. Make a list of all factors of that term.
Look at the second term. Make a list of all factors of that term.
...
Look at the nth term. Make a list of all factors of that term.
Make a new list of any prime factors present in all of the lists.
Multiply every entry in that list together and return the result.

Let's make up a new example. Say you were given 12a^4 and 7b^2

Break up 12a^4 into 12 * a^4 for convenience. Now, the factors of 12 are: 1, 12, 2, 6, 3, 4. The factors of a^4 are: a, a, a, a.
Break up 7b^2 into 7 * b^2 for convenience. Now, the factors of 7 are: 1, 7. The factors of b^2 are: b, b

Are there any factors in both lists? Let's see. Well, there's 1... and nope, nothing else. So, the GCF is therefore 1.

What if, then it was 15y^4 and 13c^4

Would the greatest common factor be 1*4, since the two different variables each are applied 4 times? (Or actually, just 4)

freemathhelpuser said:

I fail to understand why I am being told by Aleks that the greatest common factor of 15y^3 and 13c^4 is 1.

It seems it should be:
GCF of 13 and 15 = 1
y^3 and c^4 are different terms, therefore it would seem incorrect to say they have a common factor of 1 (like Aleks says it is).

Click to expand...

Since y³ = 1y³ and c⁴ = 1c⁴, Aleks (like the underlying algebra, which your class was supposed to have covered first) is correct.

freemathhelpuser said:

So the greatest common factors I would have thought would be:

1*y^3*c^4

Click to expand...

How is "y" (let alone three of them) a factor of c⁴? How is "c" (let alone four of them) a factor of y³? Please show your factorizations! Thank you!

How is "y" (let alone three of them) a factor of c⁴? How is "c" (let alone four of them) a factor of y³? Please show your factorizations! Thank you! [/QUOTE]

I don't get how it is that y is a factor of c^4 either, except that it seemed that the class was trying to teach this. you could say y*y*y, c*c*c*c and say they each appear once, but I don't see how this would be helpful at all since you are dealing with different terms.

freemathhelpuser said:

stapel said:

How is "y" (let alone three of them) a factor of c⁴? How is "c" (let alone four of them) a factor of y³?

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I don't get how it is that y is a factor of c^4 either, except that it seemed that the class was trying to teach this.

Click to expand...

You're right; y is not a factor of c⁴ (as you saw confirmed in the lesson at the link provided earlier). What, specifically, did your instructor or textbook say, which led you to think that they expected otherwise? Thank you!

freemathhelpuser said:

I fail to understand why I am being told by Aleks that the greatest common factor of 15y^3 and 13c^4 is 1.

It seems it should be:
GCF of 13 and 15 = 1
y^3 and c^4 are different terms, therefore it would seem incorrect to say they have a common factor of 1 (like Aleks says it is). So the greatest common factors I would have thought would be:

1*y^3*c^4

What am I missing.

Click to expand...

Are you perhaps getting GCF and least common multiple [LCM] confused for the y and c part of the question?

freemathhelpuser said:

What if, then it was 15y^4 and 13c^4

Would the greatest common factor be 1*4, since the two different variables each are applied 4 times? (Or actually, just 4)

Click to expand...

Did the problem by chance indicated that c and y are "relatively prime"?