What is the GCF of 180, 108, and 75?

Question

Ada Harrington · Accepted Answer

Step 1In most cases we should be able to find the GCF fairly easily by just knowing the multiplication tables up to   12  ×  12 . Sometimes a bigger number might be included which we do not know well. This is just such a case.Using factor trees mentally will allow you write all the &#039; factors.(for example:       108    =    12    ×    9    =          (      4      ×      3      )        ×          (      3      ×      3      )        =    2    ×    2    ×    3    ×    3    ×    3   )It is good to have a method available for cases when we cannot find the GCF by inspection.In order to find the GCF (and the LCM) write each number as the product of its &#039; factors.  180  =  2  ×  2  ×  3  ×  3  ×  5                    ×        ×              108    =    2    ×    2    ×    3    ×    3    ×    3    75  =  3  ×  5  ×  5  G  C  F  =  3From this it is very clear that the only common factor is 3.(I find this result surprising - I would thought it would be higher.)If we needed the LCM it can be calculated easily from this format:Include each column of factors, do not count factors that are in the same column twice.      L    C    M    =    2    ×    2    ×    3    ×    3    ×    3    ×    5    ×    5    =          2      2        ×          3      3        ×          5      2        =    2700

Brooke Webb · Accepted Answer

Step 1Factors of 180 are             {      1      ,      2      ,      3      ,      4      ,      5      ,      6      ,      9      ,      10      ,      12      ,      15      ,      18      ,      20      ,      30      ,      36      ,      45      ,      60      ,      90      ,      180      }      Factors of 108 are             {      1      ,      2      ,      3      ,      4      ,      6      ,      9      ,      12      ,      18      ,      27      ,      36      ,      54      ,      108      }      Factors of 75 are             {      1      ,      3      ,      5      ,      15      ,      25      ,      75      }      Common factors are just             {      1      ,      3      }       andGreatest Common Factor is 3.

What is the GCF of 180, 108, and 75?

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