Lesson: Find Factors of a Given Number

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Lesson Objective

SWBAT find all factors of a given number

Lesson Plan


6.NSO.N6 – Apply Number Theory Concepts including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10.


Key Points

SWBAT find all factors of a given number

·         A factor one of the numbers being multiplied in a multiplication problem

·         Sometimes factors are numbers that go into another number evenly and are sometimes called divisors 

·         Divisibility rules help us to find factors of a number


1.       List all of the factors of 36.


2.       Mr. Yeager wants to fence a vegetable garden to keep rabbits from eating his plants. The garden is rectangular and measures 72 square feet. Which of the following are the possible dimensions of the garden?

A 20 ft X 52 ft

B 15 ft X 5 ft

C 12 ft X 5 ft

D 9 ft X 8 ft


3.       List the factors of 58




Warm Up:

·         Complete below:

is 45 divisible by 5?  by 4?
2385 divisbile by 5? by 4?


·         For each number, find a value for the missing digit that will make the number divisible by 3:


41,0 __5




Intro/Direct Instruction:

·         Teacher will define factors for students while students take notes.  Discuss that many times when we are working with factors we think about a numbers’ factors in terms of factor pairs.

·         This means that you can think of two numbers that when multiplied are equal to the given number – those two numbers are factors of the given number.

·         Since factors come in pairs, one strategy for finding factors is to start with 1 and to move to each number trying to think of a multiplication fact for that number.  If you can think of one than both of those numbers are factors

·         Model:  factors of 12:  well I know that 1 x 12 = 12, so 1 and 12 are factors.  I also know that 2 x 6 is 12 so 2 and 6 are also factors of 12.  3 x 4 = 12 so 3 and 4 are also factors.  I can’t multiply anything by 5 and get 12 so 5 is NOT a factor of 12.  I can stop now because I already know 6 is a number so I’ve gone through my list.

·         Every number has 1 and itself as factor

·         Model for students writing factors in a “factor rainbow” and emphasize that “factors are friends” – they come in pairs.

·         Model finding factors for 96 (reference previous day lesson with divisibility rules and how that can help us to think of some factors of a number)


Guided Practice

·         Have students find factors for:

o    24

o    35

o    68 – highlight using divisibility rules to help us find factors


Independent Practice

·         Students complete worksheet independently finding factors of numbers


·         Define factors

·         Explain how to find factors

·         Exit Ticket


Accommodation:  Allow students to create arrays to find factors of numbers and keep numbers less than 50. 



Teach students the “Factor game”.  (30 mins)

§  We are going to learn a game called the Factor Game – some of you may already be familiar with it.  One thing that I like about this game is that the more I play it, the more things I learn and the better I become at the game.  Challenge: Since I’ve played it so many times I’m confident that I will be you all when we play it the first time. 

§  Explain that the game is played between two players, taking turns.  Player A selects a number, then player B selects all of the factors/divisors of player A’s number.  Then Player B selects a new number and player A selects all the factors of the player Bs number.

§  Explain there are some other rules that we will learn and I will explain as we play the game. 

§  First we will play as a group and I’ll go first.  Select 26 by circling it.   Ask students what numbers do you think you will get.  Remember you will get all the factors of the number I circled. 1, 2, 13.  Ask a student to keep score for us on the board.  And tally score 26 – 16. 

§  Now students should select a number and I will circle factors. 

§  Continue playing until a student picks a number with no uncircled factors left.  Explain that if you select a number with no factors left it is an illegal move – so you lose your next turn.  It’s okay to make an illegal move and you do get your points but you lose the next turn.  The game ends when there are no legal moves on the board remaining.  Player with the largest score is the winner.


Lesson Resources

Notes Factors  
Factor Game Analysis  
The Factor Game   Activity
The Factor Game
U4 L2 Notes Prime Time Factors Multiples  


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