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: 1,6 9: 1,9 The largest shared factors is 3 (GCF) 2,3 3Multiples: 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 evenlyinto another number.

Least common multiple

Smallest

Shared

The product when a numberis 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 20

10 15 201, 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 onSunday selling bracelets. She sold each bracelet for the sameamount. What is the most she could have charged for each bracelet?49 42 21 *****

1, 497

1, 422, 213, 146, 7

1, 213, 7

$7 each

Using Primes to Find the GCFYour 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)

2 3 2

2 3 3

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 66 18 and 30 32 and 48

12 66

3 4

3 2 2

11 6

11 2 3

GCF: 612 ( 3 x 4) 3 2 266 ( 11 x 6) 3 2 11

18 30

3 6

3 2 3 GCF: 6

3 10

3 2 5

18 ( 3 x 6) 3 2 330 ( 3 x 10) 3 2 5

32 48

4 8

2 2 4 2

6 8

3 2 4 2

2 2 2 2 2 3 2 2 2 2

GCF: 16

32 ( 4 x 8) 2 2 2 2 248 ( 6 x 8) 2 2 2 2 3

Guided Practice p. 10 Use any method you choose to solve these problems.

GCF8 and 32 24 and 60 3, 12, and 18 8 32 1, 8 1, 322, 4 2, 16 4, 8GCF: 8

24 60 1, 24 1, 60 2,12 2, 30 3, 8 3, 20 4, 6 4, 15 5, 12 6, 10GCF: 6

3 12 18 1, 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 toshow the multiples of eachnumber. The SMALLEST number that has each of themarks 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!!!!

1421

7

2

3

1220

4

3

5

7 is the only common prime

Be patient……one more………

12: ( 6 x 2) = 2 x 3 x 220: ( 4 x 5) = 2 x 2 x 5

We now have a complete list of all factors, butwe 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 theGCF………….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 25: 510: 2 5

2 x 2 x 5 = 20

LCM = 20

THEY SHARE NOTHING!!

3 x 5 x 7 = 15 x 7 = 105LCM = 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.

LCM7 and 9 6 and 15 39, 12, and 15They share nothing!7 x 9 = 63

LCM: 63

6: 6, 12, 18, 24, 30… 15: 15, 30, 45…

LCM: 30

39: 3 1312: 3 2 215: 3 5

615

3

2

5

391215

3 4

5

3 x 2 x 2 x 5 x 13 =6 x 10 x 13=6 x 130 = 780

13

3 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