Factors and Multiples 1.1 p. 7-10

Vocabulary Start-Up p. 7 A common factor is a number that is a factor of two or more numbers; it is shared by numbers. The largest shared factor is called the (GCF) greatest common factor. ********************************************************* The smallest (least) number that is a multiple of two or more whole numbers is the (LCM) or least common multiple of the set of numbers. Consider the numbers 6 and 9…. Factors: 6: 1,69: 1,9 The largest shared factors is 3 (GCF) 2,3 3 Multiples: 6: 6, 12, 18, 24, 30 ….. The least shared multiple is 18 (LCM) 9: 9, 18, 27……

Comparison Charts GCF Stands for Define: Greatest Common Factor LCM Stands for Define: Least Common Multiple Greatest common factor Largest Shared A number that divides evenly into another number. Least common multiple Smallest Shared The product when a number is multiplied by 1, 2, 3, 4…… Skip counting numbers…. Brian is making balloon arrangements. He has 8 blue and 12 green balloons. What is the greatest amount of identical arrangements he can make? 24

Finding Factors: p. 8 Remember how we wrote the factors in pairs? Please try to use this method! Our problem requires that we find the factors of 10, 15, and , 10 2, 5 1, 15 3, 5 1, 20 2, 10 4, 5 The greatest number of cakes in each row is 5.

Reviewing factor pairs…….. Let’s find the common factors of 60 and 90. (board) 60 90

Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? ***** 1, , 42 2, 21 3, 14 6, 7 1, 21 3, 7 $7 each

Using Primes to Find the GCF Your text shows factor trees as a way to use prime factors to find the GCF. 2 and 3 are the common prime factors. We find their product for the GCF.

Using Primes to Find the GCF You can also use something I call swim lanes to find the GCF. 12: (6 x 2) 18: (9 x 2) Notice how the common primes are lined up? 2 · 3 = 6 GCF

Your Turn p. 8 Even if you just know the GCF, use one of the methods to practice. 12 and and and GCF: 6 12 ( 3 x 4) ( 11 x 6) GCF: ( 3 x 6) ( 3 x 10) GCF: ( 4 x 8) ( 6 x 8)

Guided Practice p. 10 Use any method you choose to solve these problems. GCF 8 and and 60 3, 12, and , 8 1, 32 2, 4 2, 16 4, 8 GCF: , 24 1, 60 2,12 2, 30 3, 8 3, 20 4, 6 4, 15 5, 12 6, 10 GCF: , 3 1, 12 1, 18 2, 6 2, 9 3, 4 3, 6 GCF: 3

Least Common Multiples: Text first p. 9 Use color-coded marks to show the multiples of each number. The SMALLEST number that has each of the marks is the LCM Red and blue

This works this year…..it will not work when you have variables in the terms. Moving on……….. 1(2), 2(2), 3(3) ….. 1(3), 2(3), 3(3) ……

Here is a different way to think about this method….. Multiply what the terms SHARE by what they DON’T share. I really like this way!!!! is the only common prime

Be patient……one more……… 12: ( 6 x 2) = 2 x 3 x 2 20: ( 4 x 5) = 2 x 2 x 5 We now have a complete list of all factors, but we will not duplicate the shared factors. 2 x 3 x 2 x 5 = 60 LCM If you will remember, this is the same format we used to find the GCF………….in the set above, look for only the shared factors……. 2 x 2 = 4 GCF

Got it? p. 9 Use any method you choose…but use one! 2, 6 4, 5, 10 * 3, 5, 7 2: 2, 4, 6, 8… 6: 6, 12, 18… LCM = 6 You only need to pay attention to the 4 and 10. Why? 4: 2 2 5: 5 10: x 2 x 5 = 20 LCM = 20 THEY SHARE NOTHING!! 3 x 5 x 7 = 15 x 7 = 105 LCM = 105 If the numbers share NO COMMON FACTORS just multiply them together!

This is a very common LCM problem. Learn to recognize this type of problem. The question will involve something that WILL happen………..

Guided Practice p. 10 Use any method you choose to solve these problems. GCF 8 and and 60 3, 12, and , 8 1, 32 2, 4 2, 16 4, 8 GCF: , 24 1, 60 2,12 2, 30 3, 8 3, 20 4, 6 4, 15 5, 12 6, 10 GCF: , 3 1, 12 1, 18 2, 6 2, 9 3, 4 3, 6 GCF: 3

Guided Practice p. 10 Use any method you choose to solve these problems. LCM 7 and 9 6 and 15 39, 12, and 15 They share nothing! 7 x 9 = 63 LCM: 63 6: 6, 12, 18, 24, 30… 15: 15, 30, 45… LCM: 30 39: : : x 2 x 2 x 5 x 13 = 6 x 10 x 13= 6 x 130 = x 20 x 13= 60 x 130=780

Read what they are asking. How many movies? 4(5) = 20 20, 40, 60, 80…. 3(5) = 15 15, 30, 45, 60…… When will BOTH of these events happen? 4, 8, 12 movies