To find the greatest number of groups she can make, we are going to find the greatest common factor between the backed cookies, 100, and the brownies, 20. The greatest common factor of two numbers is the greatest number that divides the tow numbers evenly. Since Anna wants groups with the same number of cookies and brownies, she will need to divide both brownies and cookies by the greatest number that divides them both.
Remember that to find the greatest common factor (GCF) between two numbers, we first need to find the prime factors of each number, then we are going to identify the common factors, and last, we are going to multiply the least common prime factors.
Let's find the prime factors of 20 and 100 first:
[tex] 20=2^2*5 [/tex]
[tex] 100=2^2*5^2 [/tex]
Notice that the least common prime factors are [tex] 2^2 [/tex] and [tex] 5 [/tex], so we are going to multiply them to find the GCF:
[tex] GCF=2^2*5=4*5=20 [/tex]
Notice that 20, divides both 100, and 20: [tex] \frac{100}{20} =5 [/tex] and [tex] \frac{20}{20} =1 [/tex].
From that, we can infer that Angie can make 20 groups of 5 cookies and 1 brownie.
We can conclude that the greatest number of groups she can make is 20.
