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Yes. You should be able to do it over a weekend. It does take time because you have to memorize it one product at a time. After you do, you will begin to see how the numbers fit together and factoring integers will make sense. I recommend memorizing up to twelve so that you will be able to work in base twelve with ease later on.
I memorized the table by sitting with it and using two pieces of paper to cover the values I was trying to remember. This had the advantage of showing me how each multiplier progressed as the operands increased so that I began to get that glimpse of the way the system of integers is structured.
Six to eight hours of concentrated effort--one workday--should be enough to get the table so firmly ingrained that you will never forget it. The sooner you start, the sooner you will be done.