Math Problem Statement
The textbook in your class directs your students to systematically find factor pairs for a number when they are trying to find all factors. One of your students doesn’t believe this method will find all of the factors. He says, “Sometimes, I can multiply three numbers together to get another number. So, if I’m only finding factor pairs, I’m going to miss some of those factors.” Choose a number that would address your student’s concern. Demonstrate how finding factor pairs will still find the factors he is concerned about missing. Explain in a general way so that he can see this is always the case.
Solution
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Math Problem Analysis
Mathematical Concepts
Factors
Factor Pairs
Multiplication
Number Theory
Formulas
a × b = N (factor pairs)
(a × b) × c = N (multiple factors can be reduced to pairs)
Theorems
Fundamental Theorem of Arithmetic
Suitable Grade Level
Grades 5-7