You can read about prime factorization in my Oct 14<\/a>\u00a0post.\u00a0 Let’s assume you’re old hat at it now.<\/p>\n We are familiar with reducing fractions.\u00a0 For instance,<\/p>\n 40\/35=8\/7<\/p>\n We know that the reason for the reduction\u00a0is that 5 divides into both 40 and 35, so can be cancelled out top and bottom:<\/p>\n 40\/35=(8*5)\/(7*5)=8\/7<\/p>\n Of course, it’s easy to tell that 40\/35 reduces to 8\/7.\u00a0 However, what about reducing a fraction like 98\/154?\u00a0 Well, you can cut\u00a0both down by 2, then realize 7 goes into both, and so on.\u00a0 However, let’s try the prime factorization method.\u00a0 First, we’ll rewrite the fraction with each number’s prime factorization:<\/p>\n 98\/154=(2*7*7)\/2*7*11)<\/p>\n Note that 2*7 occurs in both the top and the bottom.\u00a0 It’s called the greatest common factor (the GCF)<\/strong>, since it’s the largest\u00a0combination that occurs in both prime factorizations.\u00a0 Cancel the GCF top and bottom and you get the reduced fraction:<\/p>\n (2*7*7)\/(2*7*11)=7\/11<\/p>\n Like with finding the LCM (see my Oct 17<\/a>\u00a0post), the prime factorization method for reducing fractions becomes more useful as the numbers get bigger and less familiar.\u00a0 Try it and see :)<\/p>\n