SOLUTION: Find the GCF for the folowing groups 1)48, 80 2)42,66,78 3)6y^2,15y^3 4)12a^2b,18ab^2, 24a^3b^3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the GCF for the folowing groups 1)48, 80 2)42,66,78 3)6y^2,15y^3 4)12a^2b,18ab^2, 24a^3b^3      Log On


   

Question 148869: Find the GCF for the folowing groups
1)48, 80

2)42,66,78
3)6y^2,15y^3
4)12a^2b,18ab^2, 24a^3b^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1
GCF:
First, find the prime factorization of each term:


48: 2%2A2%2A2%2A2%2A3


80: 2%2A2%2A2%2A2%2A5


Now highlight the common terms:


48: highlight%282%29%2Ahighlight%282%29%2Ahighlight%282%29%2Ahighlight%282%29%2A3


80: highlight%282%29%2Ahighlight%282%29%2Ahighlight%282%29%2Ahighlight%282%29%2A5


So the common terms are 2, 2, 2, and 2


Now simply multiply all of the common terms together to get 2%2A2%2A2%2A2=16


So the GCF is 16.



# 2

GCF:
First, find the prime factorization of each term:


42: 2%2A3%2A7


66: 2%2A3%2A11


78: 2%2A3%2A13


Now highlight the common terms:


42: highlight%282%29%2Ahighlight%283%29%2A7


66: highlight%282%29%2Ahighlight%283%29%2A11


78: highlight%282%29%2Ahighlight%283%29%2A13


So the common terms are 2 and 3


Now simply multiply all of the common terms together to get 2%2A3=6


So the GCF of 42, 66, and 78 is 6.




# 3

GCF:
First, find the prime factorization of each term:


6y%5E2: 2%2A3%2Ay%2Ay


15y%5E3: 3%2A5%2Ay%2Ay%2Ay


Now highlight the common terms:


6y%5E2: 2%2Ahighlight%283%29%2Ahighlight%28y%29%2Ahighlight%28y%29


15y%5E3: highlight%283%29%2A5%2Ahighlight%28y%29%2Ahighlight%28y%29%2Ay


So the common terms are 3, y, and y


Now simply multiply all of the common terms together to get 3%2Ay%2Ay=3y%5E2


So the GCF of 6y%5E2 and 15y%5E3 is 3y%5E2.





# 4

GCF:
First, find the prime factorization of each term:


12a%5E2b: 2%2A2%2A3%2Aa%2Aa%2Ab


18ab%5E2: 2%2A3%2A3%2Aa%2Ab%2Ab


24a%5E3b%5E3: 2%2A2%2A2%2A3%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab


Now highlight the common terms:


12a%5E2b: highlight%282%29%2A2%2Ahighlight%283%29%2Ahighlight%28a%29%2Aa%2Ahighlight%28b%29


18ab%5E2: highlight%282%29%2Ahighlight%283%29%2A3%2Ahighlight%28a%29%2Ahighlight%28b%29%2Ab


24a%5E3b%5E3:


So the common terms are 2, 3, a, and b


Now simply multiply all of the common terms together to get 2%2A3%2Aa%2Ab=6ab


So the GCF of 12a%5E2b, 18ab%5E2, and 24a%5E3b%5E3 is 6ab.