Application: Find the Greatest Perfect Square Factor
Finding the greatest perfect square factor is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 1: Numerical Expressions and Factors. Students find the largest perfect square that divides evenly into a number to simplify square roots — for example, the greatest perfect square factor of 72 is 36, since 36 x 2 = 72.
Key Concepts
When finding the prime factorization of a number, we can identify perfect square factors by looking for prime factors that appear an even number of times. A perfect square factor is formed by taking pairs of identical prime factors.
Common Questions
What is the greatest perfect square factor?
The greatest perfect square factor of a number is the largest perfect square (1, 4, 9, 16, 25, 36...) that divides evenly into that number. Finding it helps simplify square roots.
How do you find the greatest perfect square factor?
List the factors of the number, identify which ones are perfect squares, and select the largest. For example, factors of 48 include 1, 4, 16 (all perfect squares); the greatest is 16, so sqrt(48) = sqrt(16 x 3) = 4*sqrt(3).
Why is finding the greatest perfect square factor useful?
It allows you to simplify square roots completely in one step. Using the greatest (rather than any) perfect square factor gets you directly to the simplest form without needing multiple steps.
Where is this skill covered in Big Ideas Math Advanced 1?
Finding the greatest perfect square factor is taught in Chapter 1: Numerical Expressions and Factors of Big Ideas Math Advanced 1, the Grade 6 math textbook.