Congratulations on your purchase of this Really GoodStuff® Factors & Multiples Poster—a colorfulreference poster to help students define and identifyfactors and multiples and provide instruction andpractice with these important math skills.

This Really Good Stuff® product includes:• Factors & Multiples Poster, laminated• This Really Good Stuff® Activity Guide

Displaying the Factors & Multiples PosterBefore displaying the Factors & Multiples Poster,make copies of this Really Good Stuff® Activity Guideand file the pages for future use. Or, download anothercopy of it from our Web site atwww.reallygoodstuff.com. Hang the Poster wherestudents will be able to see it easily.

Introducing the Factors & Multiples PosterCall students’ attention to the Factors & MultiplesPoster. Read together the definitions for each of theconcepts and talk students through the examplesshown on the Poster. Explain that factors are thenumbers multiplied to form a product. Give exampleswith simple multiplication facts. Write a simple fact,such as 2 x 3 = 6, on the board. Explain that 2 and 3are factors of 6 because these two numbers can bemultiplied together to form the product of 6. Ask theclass if there are other ways to form 6 as a product(1 x 6). Then discuss how since 2 x 3 and 1 x 6 are theonly ways to form the product of 6, then 1, 2, 3, and 6are the only factors of 6. Using the same simple fact,explain that multiples of a number are any product(i.e. answer to a multiplication problem) that can beformed by multiplying the given number by anothernumber. Discuss how the list of multiples for a numberis endless since numbers are continuous. Explain how6 is a multiple of 2 because 6 is a product of 2 x 3.

Activities Using the Factors & Multiples PosterFinding All the Factors of a NumberBegin by asking the students if they know what aprime number is. Explain that a number is prime if itcannot be divided evenly by anything except itself and1. For example, 7 is a prime number because the onlyfactors of 7 are 1 and 7. Then ask the students if theycan think of some numbers that are not prime. Tellthem that when a number is not prime, it is compositeand, therefore, will have factors other than one anditself. The number 12, for example, is compositebecause 12 can be the product of factors other thanitself and 1: 3 x 4 = 12; 2 x 6 = 12; 1 x 12 = 12.

Discuss with the students how factors of acomposite number can be identified when there areother ways to form that number as a product besidesmultiplying the number by itself. Because 12 can beformed as a product three different ways, thenumbers used to form the product of 12 are factorsof 12: 3, 4, 2, 6, 1, and 12 are factors of 12. (Note: Thenumber 1 is neither prime nor composite since its twofactors are the same.) Show the students how tomake “factor trees” to find all of the factors of anumber. Explain that when a factor tree is made, the“evergreen branches” should continue until the bottomrow of the tree cannot “grow” any further because allof the numbers at the bottom are prime. Use theexample of 12 to show how a factor tree is made:

Factors & Multiples Poster

Helping Teachers Make A Difference® © 2008 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #156874

All activity guides can be found online:

Because 2 and 3 are prime, the factor tree stops andcannot grow any further. The factors of 12, therefore,are 1, 2, 3, 4, 6, and 12. Shown as a product of primefactors, 12 is 2 x 2 x 3.

Have students practice making factor trees withlarger numbers. Here are a few examples to getstarted. Demonstrate how some numbers, such as36, will require more than one tree because there areseveral different ways to produce the number as aproduct.

Another way to find all of the factors of a number isto make a number line showing the factors. The firststep is to list 1 on the far left, and the numberstudents want to identify the factors for on the farright (with space in between to list the factors). Thentell students to start with 2 and think if the numbercan be multiplied to get the product. If so, he should

list 2 and the number multiplied by 2 to get theproduct. Students continue with 3, 4, and so on untilall of the factors are listed. Here is an example of anumber line for finding the factors for 24 and 84:

Using the Rules of Divisibility to Find FactorsExplain that since multiplication and division facts arerelated, the rules of divisibility can be used whenidentifying the factors of a number. If necessary,teach or review the rules of divisibility with students:

Demonstrate how the rules of divisibility can be usedto help find factors of a number. Explain to studentsthat when they know one factor of a certain number,they can divide the number by the known factor to find

Factors & Multiples Poster

Helping Teachers Make A Difference® © 2008 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #156874

A number is divisible by…2 if the digit in the ones place is even.3 if the sum of the digits is divisible by 3.4 if the last two digits are divisible by 4.5 if the digit in the ones place is 0 or 5.6 if the number is divisible by both 2 and 3.7 if you can double and subtract the digit in the

ones place from the rest of the digits and theanswer is 0 or divisible by 7.

8 if the last three digits are divisible by 8.9 if the sum of the digits is divisible by 9.10 if the digit in the ones place is 0.

another factor for the number, which is called a factorpair. Here is an example of using rules of divisibility forfinding the factors for 72:

Explain that numbers greater than eight do not needto be used since after eight the factor pairs begin torepeat.

Finding the Multiples of a NumberBegin by having students skip count aloud by twos (2, 4, 6, 8…). After a few minutes, stop studentsand ask, “If we had kept going, what would the lastnumber have been?” Explain that because numbers arecontinuous and never stop, skip counting by twos (or any number) would be an endless task!

Write the first 10 numbers for skip counting by two onthe board (2, 4, 6, 8, 10, 12, 14, 16, 18, 20). Have thestudents recall the definition for a multiple from theFactors and Multiples Poster. Use the numbers onthe board to demonstrate how all of the numberslisted are multiples of 2 since they can be formed as a

product by multiplying 2 by another number. Explainthat the numbers three, five, and so on are notmultiples of two since they cannot be formed as aproduct when two is multiplied by another wholenumber. Point out that the rules of divisibility help toidentify multiples of a number. Indicate that thenumbers listed on the board are all divisible by 2, whichmakes them also multiples of 2. Remind studentsthat the multiples of a number are all the numbersthat can be divided evenly by a given number. Thatnumber, in this case, is 2. Show a few more examples,such as the ones below, of multiples of a number:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36,40…Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110…Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200 …

Point out that the first number listed is always thenumber itself and that ellipses (…) are used at theend of each list to show that the list is endless.

Number Riddles ReproducibleOnce students have grasped the concept of factorsand multiples, copy and distribute the Number RiddlesReproducible. Help students who are struggling byhelping them identify the most useful clue in eachstatement that they should begin with. For example,listing the multiples is a good place to start, thencrossing out the numbers that don’t apply, accordingto the other rules, is an efficient strategy. Tochallenge students who solve the riddles quickly,instruct them to create their own riddle, and thentest it out on scrap paper to make sure that theirriddle leads to one possible solution only. Tell thesestudents to exchange riddles and try to solve eachothers’ riddles. Answers for Number RiddlesReproducible: 12, 99, 28)

Factors and Multiples Poster

Helping Teachers Make A Difference® © 2008 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #156874

Number Is It a Factor of 72? Divide the Factor PairNumber into 72

1 Yes, all numbers are 72 / 1 1, 72 divisible by 1

2 Yes, because 72 is even 72 / 2 2, 36

3 Yes, because the sum of 72 / 3 3, 24

7 and 2 is 9, and 9 is

divisible by 3

4 Yes, 72 is divisible by 4 72 / 4 4, 18

5 No, 72 does not end in ------0 or 5

6 Yes, 72 is divisible by 72 / 6 6, 12

both 2 and 3

7 No, when I double the 2 (4) -------and subtract it from 7, the answer is not 0 or divisibleby 7

8 Yes, 72 is divisible by 8. 72 / 8 8, 9

Number Riddles Reproducible

Helping Teachers Make A Difference® © 2008 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com #156874