When we have two or more given numbers, we can find the largest factor that both numbers have in common. Step 1: We know that this is a GCF question because Maria is breaking the candy into groups and the problem using the key word 'greatest'. From the upside down division, we can see that each child would get 10 pieces of chocolate candy and 9 pieces of fruity candy. I think factor trees are one of the coolest “tools” for middle school students! This is the most obvious use of factor trees and it’s typically the first way students learn to use them. Factor trees make simplifying radicals so easy for my pre-algebra and algebra students!  Students understand that finding the square root of a number means figuring out what number times itself equals the starting number, so in simplifying radicals they are simply pulling out one of each prime factor that is listed twice in the factor tree. For students who have a tough time coming up with the numbers, I have them make a factor tree for 126.  Once they have it broken into its prime factors, they just need to break up the prime factors into 2 numbers every possible way until they find the ones with a sum of 23. Today’s lesson in my 7th grade math class was on finding the greatest common factor and least common multiple of a pair of numbers.
I started by gathering background information about what the students already knew about the GCF and LCM. Previously the students had learned to list all the factors of 2 numbers and find the largest one they had in common. Then we discussed the limitations of this method for finding the GCF and LCM, mainly the fact that if I gave them much larger numbers it would be very time-consuming to list all the factors or list multiples until they found one in common. I am looking forward to showing them how the cake method can be used to simplify fractions, too.

In this lesson we will study polynomials that can be factored using the Greatest Common Factor.
Make sure that you pay careful attention not only to the process used for factoring, but also to the make-up of the polynomials that can be factored using this method. When you factor a polynomial, you are trying to find the quantities that you multiply together in order to create the polynomial. The greatest common factor (GCF)for a polynomial is the largest monomial that is a factor of (divides) each term of the polynomial.
Before we get started, it may be helpful for you to review the Dividing Monomials lesson.
Hopefully you now understand how to factor polynomials if the polynomials have a greatest common factor.
This lesson describes the method to find the factors of a trinomial, which consists of three terms, by grouping.
In this tutorial the instructor shows how to factor a trinomial with Greatest Common Factor (GCF) and then how to group it. Because both of the numbers are even, we could start with 2.The answer goes underneath the bar.
Remember that relatively prime means two numbers that do not have any common factors other than 1. Not only is the GCF extremely important when working with fractions, but is can also be used when applying the distributive property or when solving word problems.
You can find it by listing the factors, using upside down division or by using the prime factorization.

First of all, factor out the greatest common factor (GCF), and write the reduced trinomial in parentheses.
When we see key words like largest, greatest and most combined with questions about breaking things into groups we know that we are solving a GCF question. For example, 3(3X2+2X-8) trinomial is written in the order of variable, with 3(GCF) factored out. Now identify the coefficient of the first and last terms, for example in this case, it is 3 and 8. Now choose a pair of factors whose product is equivalent to the product of first and last terms of the trinomial, and the sum is equal to the middle term, both in terms of value and sign. Rewrite the trinomial by breaking the middle term in terms of the two chosen factors, that is, 3X2 + 6x-4x _8. Now pull out the common factors for each pair ensuring that in both the pairs, we have same monomial in the parentheses.
Hence, we can find the factors of a trinomial by following the four steps viz., find the GCF, find the factors, rewrite the statement and factor by grouping.

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