Transcript Factors_and_Multiples_Notes_PP

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- 1, 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 2436Circle all factors.
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 8, 12, 18, 36
GCF=
List the factors of 1854Circle all factors.
12
1, 2, 3, 6, 9, 18,
1, 2, 3, 6, 9, 18, 27, 36,
GCF=
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 number
83157-
8, 16, 24, 32, •40
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- 24, 48, 72, 96, 120
36- 36, 72, 108, 144, 180
Circle all multiples.
LCM=
72
List 5 multiples of 16- 16, 32, 48, 64, 80, 96, 112,
14- 14, 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:
8-
13-
51-
No
Yes
No
1-
Neither
19-
Yes
List the first 15 prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Prime Factorization-
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): Divide the given number
by prime numbers from
96 ÷ 2 = 48
smallest to largest until the
last number is one.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6÷2=3
3÷3=1
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.
96
120
2x2x2x2x2x3 = 96
5
8
2 4
4
2
2
2
3
2
10
or 2 x3=96
12
5
2x2x2x3x5=120
3
12
2
3
or 2 x3x5=120
4
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:
12- 12, 24, 36, 48, 60,
16- 16, 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:
Question:
Diagram:
Estimate:
Problem and Answer:
Final Answer:
Jar of Peanutbutter has 72 servings.
Jar of Jelly has 40 servings
How many days will it take to
have both jars run out at the
same time?
72- 72, 144, 216, 288, 360,
In between 72 and 400 days
40- 40, 80,120, 160, 200, 240, 280,320,360,
LCM is 360
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:
Estimate:
Redline- 6:00,7:00, 8:00, 9:00, 10:00, 11:00, 12:00,
Between 1 and 12
1:00, 2:00, 3:00, 4:00, 5:00, 6:00,
Problem and Answer:
Final Answer:
They will meet 6 different times.
Blueline- 6:00, 6:40, 7:20, 8:00, 8:40, 9:20, 10:00,
The first time they will meet is 8:00 AM
10:40 ,11:20,12:00, 12:40, 1:20, 2:00, 2:40, 3:20,
4:00, 4:40, 5:20, 6:00
Exponent-The number of times a number is multiplied by itself.
3
Ex:3x3x3 = 3 = 27
3
2
2
2x2x2x3x3x5x5x7x9 = 2 x 3 x 5 x 7 x 9 = 113400
x
To use your calculator to answer exponents, use the y button
4
Ex: 3
would be typed as
3 then yx
then
4
then =
81
Examples
5
2
3 x 7 = 11907
2
2
2
5 x 7 x 11 x 13 = 1926925