Finding the Greatest Common Factor

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Big Idea



15 minutes

The students will be working on an illustrative math problem involving types of numbers.  Their job is to decide, based on definition, whether a number is:

FACTOR: a number that divides evenly into another number

PROPER FACTOR: all factors except the number itself

PERFECT NUMBER: the sum of all of its proper factors is equal to the number itself

DEFICIENT NUMBER: the sum of all of its proper factors is less than the number itself

PRIME NUMBER: only factors are one and itself

ABUNDANT NUMBER: the sum of all of its proper factors is greater than the number itself

I chose this problem because it introduces students to finding factors, but it also has them looking at vocabulary words and applying their meaning to the numbers (SMP 2)

As students finish, allow them time to compare their answers with a partner.  Be sure to remind them that they need to convince their partner that their answer is correct (SMP 3)

Direct Instruction

30 minutes

During the direct instruction, I will be teaching the students two strategies to use to find the GCF.  Many people are familiar with the making the list strategy and although it’s very easy to use, it can become complicated as the numbers get larger.  Also, for students that are not very good with the multiplication facts this strategy will not work. The other strategy that I’m teaching the children is to use the ladder.  The ladder has them placing the 2 numbers in the division house.  They pull out a common factor.  I tell the students to use 2,3,5 first because those are the most common prime numbers.  However, any number that is a factor will do.  They divide each number by the factor and put the 2 new numbers below the original.  We call this a new step. Looking at the 2 new numbers, they will need to decide if they have a common factor.  If they do, then they divide both numbers again.  If the only common factor is one, then they can stop and multiply the steps together to find the GCF.  Students are using their knowledge of divisibility rules to help them find a number.  It’s easy to use because they are dividing by smaller numbers.  (see the power point for a visual on how to do this)  I’ve used this strategy with my lower functioning students and they really get it.  

Finding the GCF using the list and ladder supports SMP 4 and 5 because they are modeling their math using the ladder and list as a tool.

Identify the factors supports SMP 2.

Using the divisibility rules to find a factor supports SMP 6

Around the Room

30 minutes

Students will be working on a structure called Around the room.

The students need a piece of paper with space for 15 answers and work. Students will be working in pairs.  Partners need to discuss answer before moving on to another questions.  The work papers can be collected as evidence of student learning. 

I created a power point for the GCF problems.  I figured it would be easy to print out the slides to use for the questions in the around the room.


10 minutes

Students will be completing a comprehension menu so I check for their level of understanding.  This is a differentiated activity and it is a good idea to have the students place a mark in the box they felt most comfortable answering.