To be able to think of numbers in
factored form one must master the multiplication facts. Students should
not only know that 8 x 7 = 56, but also should recognize when given the
number 56 that it factors (breaks up) as 8 x 7. Requiring this next
level motivates the student to get beyond using repeated addition to do
multiplication problems. Being able to think this “factoring” way
obviously makes division much easier.

After learning some divisibility rules, how to
divide with a one-digit number, and the relationship between
multiplication and division, students can factor numbers like 65. First
they recognize that since it ends in the digit 5, it is divisible by 5.
Dividing 65 by 5 yields 13, so they know that 65 = 5 x 13.

The REAL benefit of factoring comes in working
with fractions. Fractions are so much easier to work with when we use
factoring to help. We can use factoring to help reduce fractions to
lowest terms, to help simplify multiplication and division problems, to
find a common denominator when adding and subtracting fractions, and
then to complete the addition and subtraction problems.

Working with fractions in this way helps
students make the transition from basic mathematics to algebra. In
algebra we factor algebraic expressions and use this to solve, not only
problems involving fractions, but also problems in simplifying radical
expressions and solving polynomial equations of degree two or higher.