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Find the GCFof each set of numbers.

 

(a) 36, 90

(b) 16, 24, 40

 Mar 18, 2021
 #1
avatar+141 
+1

i'm not really sure how to explain this, but if you are new to solving the GCF, an easy way to do this is to just list out all the factors of the numbers.

 

this method works best for smaller numbers. sometimes, you can occasionally tell the GCF of some numbers just by first glance. if you are interested in other (more effective) methods, feel free to ask!

 

a)

factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

 

as you can see, they both share the common factor 18, so the GCF of 36 and 90 would just be 18.

 

b)

factors of 16: 1, 2, 4, 8, 16

factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

 

as you can see, they both share the common factor 8. they also share other factors, like 1, 2, and 4, but 8 is the largest one. so the GCF of 16, 24, and 40 is 8.

 

 

hope this helped! please let me know if you still have any further questions. :)

 Mar 18, 2021
 #2
avatar+118015 
+1

Thanks, Idyllic....here's  another  method

 

36  =   2^2 * 3^2

90  =   2 * 3^2  *  5

Look at the  prime factors  that are common to  each each  =  2  and 3

Take  each  with their  lowest powers    =  2 * 3^2  =  2 * 9  =  18  =  GCF

 

16 =  2^4

24 = 2^3 * 3

40  = 2^3 * 5

Only  common prime to each = 2

Lowest power  =  3

GCF  = 2^3  =  8

 

 

cool cool cool

 Mar 18, 2021

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