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Find the greatest common factor.$$4 y, 28$$...

Question

Find the greatest common factor.$$4 y, 28$$

Find the greatest common factor. $$4 y, 28$$



Answers

Find the greatest common factor.
$$4 y, 28$$

Okay. We need to find the greatest common factor of these three expressions. 27 y squared 45 like you'd and 99 in the fourth. So we're gonna begin with prime factories. Ation here we have three times. Nine. You break that down further. That nine this three times tree. So we have three times. Three times three is 27 for 45. We have five times nine. You break the nine again. So we have five times. Three times three for the nine. You just have to break it to three times three. So it is just three times three. Now, if you look at these three prime factories ations look for what they have in common. You see that each of the expressions has three times three or nine. So my greatest common factor is gonna be nine. Now, we feel looking are variables. I have to wise here. I have three wise here, and I have four was there, so I could find why times Why in every single expression, See right there. So when you start to look at the exponents, you'll quickly get to a place where you don't necessarily need to write out the expanded form of the variables. So why squared or white times? Why this part? The variable part of my greatest common factor. So my greatest common factor for those three expressions is nine. Why squared?

To find the greatest common factor we will factor both ate a and 72 8 a is two times two times two in times A in 72. Let's see, I can divine 72 by two, which will give me 36. I divide that by two Azumi 18 I divide that by two Azumi nine and nine. This three times three. So, really, I have three pairs of twos and that's it. So two times two times two, which the G. C F is.

Two factor by using the greatest cone factor. We need to go ahead factor both terms, and we'll just do the positive form of these terms. So seven x 38th this seven times. And then there's eight. X is in 28 x to the third. I should put extra. The third here is Ah, this is two times 2 10 7 and then three exes. So we have a common seven and then three exes in common seven x to the third power is our g cf too fat. Now this DCF is negative because the leading coefficients negative. So we'll do negative seven x cubed. So this factor in a negative seven x cubed out. Now that makes this negative seven a one and this extra the eighth. If you take three exes away, will be X to the fifth This negative this negative factor Divide Negus 20 by negative 70 Get a plus four and the three exes air gone because you factor them out. So here's our answer

All right on this problem. We're looking at factor at the greatest common factor. So we're looking for a term that goes into both of thes terms. So we're looking for something that can divide out of both of them. Um, so in this case, we can look at the 16 and 24. We can know that two goes into both of them. Um, we can see. Hopefully, you know that Ah, four goes into both of them. So four times for 16 4 times six is 24. But the greatest common factor is the number eight. So that's the number we're gonna take out taking out an eight here. And we ask yourselves, what is left won't are factoring. Um, it's really a form up division. So I'm asking myself if I were to divide out and ate up here. 16 by the bay is a two. Um, the X just kind of stays along because 16 x divided by a day. Only a number is affected, and then 24 divided by eight is a three. So we take out a term only factor out of term. Really? We're just dividing it out to the front It's really the reverse of distributing, so case you can see this eight Outside of the parentheses you distribute through. This is taking out in a so it's un distributing. Factoring out a term it's our answer for this one is eight parentheses to expire history.


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