L.C.M. is "least common multiple"- the smallest quantity that is a multiple of both (or all) numbers or expressions. H.C.F. is highest common factor (I would say "gcd"-greatest common divisor). It is the largest number or expression that divides all given numbers or expressions.

16= 8*2 and 24= 8*3 so 8 is the largest number that will divide both 16 and 24. 16ab has one but not two factors of "a" and 23a^2 does not have a "b" so the H.C.F of 16ab and 24a^2 is 8a.and what is the H.C.F. of

16ab and 24a^2

Although you didn't ask, the L.C.M. is 48a^2b.

How "methods" are there to divide numbers? There really only one "method"- old fashioned "long division". So called "synthetic division" is just a version of that for very simple cases.another question is :

how many methods to divide a polynomials in x by another polynomials in x?

and what are the methods? I really forget these things

By the way, is there any websites that explain some general concepts like the above? Because I have become a mathematics teacher recently, I hope to review some resources to help me recall some simple concepts and learn the way to explain to my students

Thanks all