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:
241, 2, 3, 4, 6, 8, 12, 24
36-
1, 2, 3, 4, 6, 9, 12, 18, 36
51-
1, 3, 17, 51
72-
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

List the factors of 24-
1, 2, 3, 4, 6, 8, 12, 24
361, 2, 3, 4, 6, 8, 12, 18, 36
Circle all factors. GCF= 12
List the factors of 18-
1, 2, 3, 6, 9, 18,
541, 2, 3, 6, 9, 18, 27, 36,
Circle all factors. GCF=
18

You will have many multiples!!!

8-
8, 16, 24, 32, • 40
3-
3, 6, 9, 12, 15
15-
15, 30, 45, 60, 75
7-
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 2424, 48, 72, 96, 120
3636, 72, 108, 144, 180
Circle all multiples. LCM=
72

List 5 multiples of 1616, 32, 48, 64, 80, 96, 112,
1414, 28, 42, 56, 70, 84, 98, 112, 126, 140
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.
Circle all multiples. LCM=
112

Prime Factors- Prime factors are numbers that can only be divided by 1 and itself.
State whether the following numbers are prime:
813511-
No Yes No Neither
19-
Yes
List the first 15 prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

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

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
Divide the given number by prime numbers from smallest to largest until the last number is one.
96 = 2 * 2 * 2 * 2 * 2 * 3

EXAMPLE 2. Prime factorization of 96 (by branching):
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.
120
2
4
2
8
96
2 4
12
2x2x2x2x2x3 = 96
5 or 2 x3=96
3
2 2
5
10 12
2 3 4
2x2x2x3x5=120
3 or 2 x3x5=120
2 2

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:
Last occurred together in 1963
Tornados occur every 12 years
Blizzards occur every 16 years
Diagram:
1212, 24, 36, 48, 60,
1616, 32, 48, 64, 80
Problem and Answer:
They occur together every 48 years.
It last occurred in 1963.
1963 + 48= 2011
Question:
When will they occur together again?
Estimate:
Within a range of 10 to 60 years.
Final Answer:
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:
Jar of Peanutbutter has 72 servings.
Jar of Jelly has 40 servings
Diagram:
7272, 144, 216, 288, 360,
4040, 80,120, 160, 200, 240, 280,320,360,
How many days will it take to have both jars run out at the same time?
Estimate:
In between 72 and 400 days
Problem and Answer:
LCM is 360
Final Answer:
It will take 360 days to run out of both jars at the same time.

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:
Redline Bus takes 60 min. to complete route
Blueline Bus takes 40 min. to complete route
Question:
How many times throughout the day will they meet? When is the first time they will meet?
Diagram:
Redline- 6:00,7:00, 8:00, 9:00, 10:00, 11:00, 12:00,
Estimate:
Between 1 and 12
1:00, 2:00, 3:00, 4:00, 5:00, 6:00,
Problem and Answer:
10:40 ,11:20,12:00, 12:40, 1:20, 2:00, 2:40, 3:20,
4:00, 4:40, 5:20, 6:00
Final Answer:
Blueline- 6:00, 6:40, 7:20, 8:00, 8:40, 9:20, 10:00, They will meet 6 different times.
The first time they will meet is 8:00 AM

Exponent-The number of times a number is multiplied by itself.
Ex:3x3x3 = 3
3
= 27
3 x
2
2x2x2x3x3x5x5x7x9 = 2 3 x 5
2 x 7 x 9 = 113400 x
To use your calculator to answer exponents, use the y button
Ex: 3
4 would be typed as
3 then y x then
4 then = 81

3
5
7
2 x = 11907
Examples
5
2 x
2
7 x 11
2 x 13 = 1926925