This document provides instructions for using prime factorization to find the greatest common factor (GCF) and least common multiple (LCM) of numbers. It describes factor trees and the "cake method" for writing numbers as products of prime factors. Students practice finding the prime factorizations of various numbers and using them to calculate GCF and LCM. The document uses examples and explanations to teach these concepts.

12. Find and write the prime factors of a number. Use prime factorization to solve problems.
Title page.
Play this prime factor game to review prime numbers. Divide the class into 2 teams. Teams take it in turns to name the prime number covered
by either a 1-point or a 2-point square. If they are correct, they can drag the square into the their total column. If they are incorrect, the square
goes into the trash. In the event of a tie, the team that can name the first prime number greater than 500 wins (503).
"What is prime factorization?" (A number written as the product of its prime factors.) Ask student volunteers to use the cloned branch and the Pen
Tool to find the prime factorization of 24 and 42 using the factor tree. Ask students to write their answers using exponents. Drag the icon from the
right to check the answers.
Introduce the "cake method" as another strategy to find prime factorization. Using this method, we keep dividing the target number by prime
numbers until the quotient is 1. Explain that we could start with any prime number, but the smallest prime number that will go into the target
number is often used. Divisibility tests can help identify this. Click to animate each step.
Practice using the cake method to write the prime factorization of 660.
Solution to page 5.
Ask students to use either the factor tree or cake method to find the prime factorization of 924.
Use prime factorization to find the GCF and the LCM for 198 and 660. Explain to students that to find the GCF, find the factors that are common to
both 198 and 660 and multiply them together. To find the LCM, count the number of times each factor appears in the prime factorizations of 198
and 660, and then multiply together the highest count for each factor. Use the icons to identify the factors.
Solution to page 8.
A contextual question. Students are often confused about whether they need to find GCF or LCM to solve problems. Explain that the question
provides us with a hint: we have been asked to find the greatest number of packs, and so it's GCF we need to find. We can then use simple
division to answer the second part of the question.
Solution to page 10.