what is the highest common factor of 33, 66, 88, 132 

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As a fifth grade teacher, I like to tell my students to create "T" charts to find the Greatest Common Factor between numbers.  

For your problem, you would create four capital letter Ts and place 33, 66, 88, and 132 on top of the horizontal part of the T.  I suggest to my students to write first the number one on the left hand side of the vertical part of the T.  On the right hand side, the students will write the number that is on top.  This is due to the Identity Property of Multiplication, which states that any number multiplied by one is that number.  

Next, I have my students see if two is a factor of the number of top.  I remind them that if a number is an even number, then two is a factor of the number that you are finding the factors of.  We continue to work through the rules of multiplication until we find a double or the numbers on either side of the T are one whole number away from each other.  

After all of the factors have been listed for each of the numbers, I have my students circle the factors that are the same in all of the T charts (in your case all 4).  

After circling the common factors, we look to see which number is the greatest in value.  This number is your Greatest Common Factor (11 for your problem).

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Another way to find GCF of several numbers is by using their prime factorizations:

`33 = 3*11`

`66 = 2*3*11`

`88 = 2^2*11`

`132 = 2^2*3*11`

The greatest common factor is then found by multiplying all common prime factors found in all numbers. As can be seen from the prime factorizations above, 11 is the only prime factor present in all four numbers. Therefore GCF = 11.

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To find the GCF, first, list all the factors of all the numbers.  Such as, for 33, we would have 1, 3, 11, and 33, since 1*33 = 33 and 3*11 = 33.  For all the numbers, we would have:

33 - 1, 3, 11, 33

66 - 1, 2, 3, 6, 11, 22, 33, 66

88 - 1, 2, 4, 8, 11, 22, 44, 88

132 - 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

Now, what number is the greatest that is common for all 4 numbers.  33 doesn't appear in all four numbers, so that doesn't work.  22 doesn't work.  In all 4 numbers, 11 is the highest number common to all.  So, 11 is the GCF.

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