SOLUTION: What is the Greatest common factor of 36,54,81,99

Here is how to find both the GCF and the LCM:

Break them all into primes:

36 = 6×6 = (2×3)×(2×3) = 2×2×3×3
54 = 9×6 = (3×3)×(2×3) = 2×3×3×3
81 = 9×9 = (3×3)×(3×3) = 3×3×3×3
99 = 9×11 = (3×3)×11 = 3×3×11

Now line up the factors so that there are only like factors
in each column, like this:


 36 = 2×2×3×3
 54 =   2×3×3×3
 81 =     3×3×3×3
 99 =     3×3    ×11
--------------------
GCF =
LCM =

For the GCF bring down only the columns that
have no skips, that is, that are common to all,
that is, those ehich have 4 in them,
which are the two columns of 4 3's:

 36 = 2×2×3×3
 54 =   2×3×3×3
 81 =     3×3×3×3
 99 =     3×3    ×11
--------------------
GCF =     3×3


For the LCM bring down EVERY column:

 36 = 2×2×3×3
 54 =   2×3×3×3
 81 =     3×3×3×3
 99 =     3×3    ×11
--------------------
GCF =     3×3
LCM = 2×2×3×3×3×3×11

Now multiply to get the GCF and the LCM

 36 = 2×2×3×3
 54 =   2×3×3×3
 81 =     3×3×3×3
 99 =     3×3    ×11
--------------------
GCF =     3×3        = 9
LCM = 2×2×3×3×3×3×11 = 3564

Edwin