Factors and Multiples

Factors-

Factors are numbers that are multiplied together to get a final number. (You will eventually run out of Factors)You will have a Final Factor

Stop looking for factors when the number you divide by is larger or equal to the number in your answer.Ex. 24 divided by 4 = 6, 24 divided by 5 = 4.8 You do not have to go beyond this point because your next number is 6 and we already have 6 as a factor.

List factors of the following numbers: 24-

36-

72-

51-

1, 2, 3, 4, 6, 8, 12, 24

1, 2, 3, 4, 6, 9, 12,18,36

1,3, 17, 51

1, 2, 3, 4, 6, 8, 9, 18, 24, 36, 72

Greatest Common Factor (GCF)-GCF is the largest factor that is common of two or more numbers

Circle all factors. GCF=

List the factors of 24-

36-

List the factors of 18-

54-

Circle all factors. GCF=

1, 2, 3, 4, 6, 8, 12, 24

1, 2, 3, 4, 6, 8, 12, 18, 36

121, 2,

1, 2,

3,

3,

6,

6,

9,

9,

18,

18, 27, 36,

18

Multiples-

Multiples are the result of multiplying two numbers. (You will never run out of Multiples)

You will have many multiples!!!

List the first five multiples of each given number8-

3-

15-

7-

•4032,24,16,8,

3, 6, 9, 12, 15

15, 30,45, 60, 75

7, 14,21,28,35

Lowest Common Multiple (LCM)-LCM is the smallest common number that has two or more numbers that it can be divided by

List 5 multiples of 24-

36-

24, 48, 72, 96, 120

36, 72,108, 144, 180

Circle all multiples. LCM=72

List 5 multiples of 16-

14-

Circle all multiples. LCM=

If you cannot find the LCM after the first five numbers of each group, then start again with the smaller number and continue with 5 more until you find the LCM. If you still can’t find the LCM do 5 more with the larger number.

16, 32,48,64,80,96,112,

14,28,42,56,70,84,98,112, 126,140

112

8- 13- 51- 1- 19-

State whether the following numbers are prime:

List the first 15 prime numbers:

Prime Factors- Prime factors are numbers that can only be divided by 1 and itself.

Yes YesNoNo Neither

472, 3, 5, 7, 11, 13,17, 19,23,29,31,37,41,43,

A process in which a list of prime numbers is found that when multiplied together form a given number

Prime Factorization-

EXAMPLE   1.   Prime factorization of 96 (by division):

96 ÷ 2 = 48

  48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

  6 ÷ 2 = 3

3 ÷ 3 = 1

96 = 2 * 2 * 2 * 2 * 2 * 3

Divide the given number by prime numbers from smallest to largest until the last number is one.

EXAMPLE   2.   Prime factorization of 96 (by branching):

120

Another way to approach the task is to choose ANY pair of factors and divide these factors until all the factors are prime. Circle the numbers as they become prime.

96 2x2x2x2x2x3 = 96 5

or 2 x3=968 12

4 2 4 3

2 2 2 2

10 12

5 2 3 4

2 2

2x2x2x3x5=120 3

or 2 x3x5=120

Billy doesn’t like severe weather! The weather station tells him that blizzards occur every 16 years in Ohio. The station also tells Billy that severe tornado seasons occurred every 12 years. The station showed clips of 1963 when both blizzards and tornadoes occurred. When is the next time that both of these groups should appear together?

Information: Question:

Diagram: Estimate:

Problem and Answer: Final Answer:

Last occurred together in 1963Tornados occur every 12 years

Blizzards occur every 16 years

When will they occur together again?

Within a range of 10 to 60 years.16-

12- 60,48,36,24,12,

They occur together every 48 years.It last occurred in 1963.

1963 + 48=2011

80 16,32,48,64,

They will occur together again in 2011.

Don loves peanut butter and jelly sandwiches. One day while he was eating, he noticed that each jumbo jar of peanut butter has 72 servings, but the jelly jar has only 40 servings. If he opened the jars on the same day and used exactly one serving each day, how many days would it take until he emptied a peanut butter jar and a jelly jar on the same day?

Information: Question:

Diagram: Estimate:

Problem and Answer: Final Answer:

Jar of Jelly has 40 servingsJar of Peanutbutter has 72 servings. How many days will it take to

have both jars run out at the same time?

72-40-

72,144,216,288,360,80,120,160,200,240,280,320,360,

In between 72 and 400 days

It will take 360 days to run out of both jars at the same time.

LCM is 360

40,

The red line bus takes 60 minutes to complete its route from the time it leaves from and returns to the station. The blue line bus takes 40 minutes to complete its route from the time it leaves from and returns to the station. If both buses begin their routes at 6:00 a.m., how many times throughout the day will they meet at the station at the same time, if the busses stop running at 6:00 p.m.? When is the first time they will meet? Make a chart to show the times both buses are at the station at the same time.

Information: Question:

Diagram: Estimate:

Problem and Answer: Final Answer:

Redline Bus takes 60 min. to complete routeBlueline Bus takes 40 min. to complete route

How many times throughout the day will they meet? When is the first time they will meet?

Between 1 and 12Redline-6:00,7:00,8:00,9:00,10:00,11:00,12:00,

1:00,2:00,3:00, 6:00,4:00,5:00,

Blueline-6:00,6:40,7:20,8:00,8:40,9:20,10:00,

,11:20,12:00,12:40,1:20,2:00,2:40,3:20,4:00,4:40,5:20,6:00

They will meet 6 different times. The first time they will meet is 8:00 AM10:40

Exponent-The number of times a number is multiplied by itself.

Ex:3x3x3 =33

=27

2x2x2x3x3x5x5x7x9 =2 3 x3 2

x52

x 7x 9 =113400 x

To use your calculator to answer exponents, use the y button

=Ex: 34

would be typed as 3 yx 4then thenthen 81

Examples

7 x2 2

112

x13x = 19269255

75 2

x = 119073