Question 770758: My child is in 9th Grade homeschool she can not pass to 10th grade until she can understand her math ,but she is having a lot of trouble with it.One of the problems is,Find the GCF of each pair of monomials;then write each monomial as the product of the GCF and the remaining factors of that monomial.1)38m and 57n
2)10c>2d and 15cd>2 Thank You.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! My youngest son attended school online from home for 7th-12th grades via a charter school (CCA). Luckily, I was qualified to help him on most subjects, but it was good to have teachers to objectively grade his work, and help him in ways that I could not help.
GCF = Greatest Common Factor
One strategy to find the GFC is to split each number or expression into factors as much as you can. We call that factoring completely.
For example, 15 is the product of 3 times 5, and 15cd is the product of 3, 5, c, and d, all multiplied together:
A number like 2, 3, 5, or 19, that can only be evenly divided by itself and by 1, is called a prime number. Still, it can be written as the product of 1 and itself, as in  .
In the factoring, we can always include a 1. It is not usually written out, but we all understand that 1 is a factor of any expression except zero.
So the complete factorizations for the expressions you list are like this:
Once the expressions are factored you look for common factors in the factorizations. If there seems to be none, you use 1 as a common factor. If you find more than one common factor, then the product of the common factors found is a common factor.
I believe the answers you needed are:
Extra examples of common factors:
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