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what is the gcf of 12, 16

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3 Answers

If you break a number down to it's prime factorization you can always determine the GCF.
What that means is you write the number as the product of only prime numbers. 
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
 
Remember the C in GCF means Common
What do 12 and 16 have in common?
2 * 2  or 4
 
There are a couple of ways to figure out the GCF. One is just trying out what 12 and 16 are both divisible by.
 
12 can be divided by 12, 6, 4, 3, 2, and 1
16 can be divided by 16, 8, 4, 2,  and 1
 
You can compare and see that the largest number they both have is 4.
 
You can also do a factor tree for each number and see how many prime numbers you have in common for both.
 
You do a factor tree by dividing the number into smaller numbers and dividing those until you can't divide anymore.
 
A factor tree for 12 is -  
 
      12
     2  6
       2  3
 
A factor tree for 16 is -
 
     16
    2   8
       4  2
      2 2
 
They both have 2 sets of 2 in common, 2 * 2 = 4