Factors and Multiply

Factors & Multiples

Chapter 2 Review

GCF and LCM

Factors and Multiples

Form One

Factors

5 and 7 are the FACTORS of 35

35 is the MULTIPLE of 5

35 is the MULTIPLE of 7

Common Factor of 16 and 24

ANSWER IS 8

Highest Common Factor(HCF) OF 18 AND 24

ANSWER IS 6

Multiple Choice

List the factors of 49.

• 1,3,5,7

• 1,7,49

Multiple Choice

List the factors of 78.

• 1,2,3,6,13,26,39,78

• 1,2,3,7,8

Multiple Choice

List the multiples of 3.

• 3,5,7,9,11,13,...

• 3,6,9,12,15,18,...

Multiple Choice

List the multiples of 7

• 1,7,.....

• 7,14,21,28,35,.....

Open Ended

List the smallest prime number.

Open Ended

Calculate the common prime factor of 21 and 24.

(Factor Tree Method)

Open Ended

Calculate the highest common factor of 18 and 30.

(Repeated Division)

Open Ended

Calculate the lowest common multiple of 12 and 18.

It is given that 5 is a factor of the number P, and P is a factor of 75.

State all the possible values of P.

-->P is the multiple of 5

-->P is a factor of 75

The numbers 84, 108 and 192 are divisible by Q exactly.

What is the greatest possible value of Q?

• 84,108和192可以被Q整除。

• 找Q的最大值。

• 从中，得知道Q就是84，108和192的factor

Calculate the Common Multiple of 9 and 12.

Calculate the first 3 common multiple of 9 and 12

• 用Repeated Division或Prime Factorization找出LCM

• 因为LCM是9和12的第一个共同的倍数（multiple）

• 首五个相同的倍数：1 X LCM，2 X LCM，3 X LCM

• LCM是36； 1X36,2X36,3X26

• First 3 common multiple are 36,72,108

Multiple Choice

List the multiples of 3.

• 3,5,7,9,11,13,...

• 3,6,9,12,15,18,...

Factors and Multiples

Let's try something new!

GREATEST

COMMON

FACTOR

• To find the GREATEST COMMON FACTOR, we use the prime factorization and look for over lapping prime factors

• OR you can list all the factors and find the LARGEST factor that overlaps (this is risky, because it is easy to forget a factor)

• Numbers with no factors in common have a GCF of 1

Multiple Select

Select all factors of 6

• 1

• 2

• 3

• 4

• 6

Multiple Select

What is the prime factorization of 18?

• 2 x 2 x 2 x 3

• 2 x 3 x 3

• 3 x 3 x 3

• 6 x 3

Multiple Choice

What is the greatest common factor of 12 and 18?

• 2

• 4

• 12

• 6

LEAST

COMMON

MULTIPLE

• To find the least common multiple, list several multiples of each number and circle the SMALLEST number they have in common!

• Numbers that are "relatively prime" have no factors in common and their product will be the least common multiple.

Multiple Select

Check all boxes that show a multiple of 8.

• 8

• 12

• 16

• 24

• 30

Multiple Choice

What is the least common multiple of 8 and 6?

• 14

• 12

• 48

• 24

Multiple Choice

What is the least common multiple of 7 and 9.

• 16

• 54

• 63

• 81

GCF/LCM word problems

• If it asks for the "maximum" or the "largest number of groups", you will use the GCF

• If you are looking for overlapping dates or amounts that are bigger than the numbers given, you will use the LCM

• Think about what is "reasonable"

Multiple Choice

Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes. If he has 20 blueberries and 30 grapes, what is the maximum number of bags of snacks that he can pack so that each bag has the same number of blueberries and grapes?

(hint, use the greatest common factor)

• 5 bags

• 10 bags

• 50 bags

• 60 bags

Multiple Choice

On James’s MP3 player, he has 12 sad songs and 40 upbeat songs that he wants to put into playlists. He wants to have the same number of sad songs and upbeat songs in each playlist. What is the maximum number of playlists that he can create?

• 2 playlists

• 3 playlists

• 4 playlists

• 10 playlists

Multiple Choice

Fresh produce is delivered to a restaurant every 4 days. Every 6 days, the restaurant receives a delivery of dried and canned goods. If the produce and dried and canned goods were delivered today, how many days will pass until they are all delivered to the restaurant on the same day again? (hint, we are looking for overlap, use LCM)

• 2 days

• 6 days

• 12 days

• 24 days

Multiple Choice

Miki has 104 nickels and 88 dimes. She wants to divide her coins into groups where each group has the same number of nickels and the same number of dimes. What is the largest number of groups she can have?

• 13

• 11

• 8

• 4

Multiple Choice

The manager of a snack bar buys bottled water in packs of 35 and candy bars in packs of 20. Then, she sells the items individually. Yesterday, she bought the same number of water bottles as candy bars to sell at the snack bar. If she bought the lowest number of items possible, how many packs of each item did she buy? (hint she is try is looking for an overlapping number, use LCM- then see how you got to the LCM)

• 5 packs of water and 5 packs of candy

• 4 packs of water and 7 packs of candy

• 8 packs of water and 14 packs of candy

• 20 packs of water and 35 packs of candy

Poll

How confident do you feel about Factors and Multiples

• confident

• mostly confident

• I could use more practice

• I need a lot more practice

Factors, Factor Pairs, Prime, and Composite Numbers

​

This week we talked about factors!

• Factors are the numbers you can multiple to get another whole number.

• You can list factors two ways: 1. with their pair (the number you multiple it by to get the larger number, or 2. in a list from least to greatest

Multiple Choice

Is 3 a factor of 21?

• yes

• no

Multiple Select

Check all the correct answers.

Which of the following numbers have 5 as a factor?

• 15

• 20

• 25

• 32

Multiple Select

Check all the correct answers.

Which of the following numbers have 2 as a factor?

• 8

• 10

• 15

• 24

Now we need to talk about PRIME and COMPOSITE numbers!

​

Prime Numbers

• Prime Numbers only have two factors: 1, and themselves!

• No other numbers can be multiplied together to get that prime number

• Prime numbers from 0-100 are:

• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Compsite Numbers

• The are the OPPOSITE of prime

• Composite numbers have MORE than two factors!

• The easiest way to check if a number is composite is:

• to check if it is even, if so 2 will be one of its factors and it would be considered composite

• if that isn't the case, see if it ends in 0 or 5, if so 5 would be one of its factors and it would be composite

• if it isn't even (ending in 0, 2, 4, 6, or 8) and it doesn't end in 5... then you need to check your multipication chart to see if 3, 4, 6, 7, 8, or 9 is one of that numbers factor's!

But what about ZERO?

The number 0 is not considered prime or composite!

Open Ended

What have you learned through this lesson today?

All of the highlighted numbers in this chart are PRIME! Their only factors are 1 and themselves.

Multiple Choice

Composite numbers have

• no factors.

• one factor.

• two factors.

• three or more factors.

Multiple Choice

A prime number has

• one factor.

• two factors.

• three or more factors.

Multiple Choice

Is 35 prime or composite?

• prime
• composite

Multiple Choice

is 5 prime or composite?

• prime
• composite

Multiple Choice

Is 12 prime or composite?

• prime
• composite

Multiple Choice

Which number below is a prime number?

• 1
• 0
• 2
• 9

Multiple Choice

True or False
0 is a COMPOSITE number.

• TRUE
• FALSE

Multiple Choice

Find the prime number.

• 0
• 1
• 7
• 4

Multiple Choice

the only factors prime numbers have are:

• 0 and 1
• 0 and itself
• 1 and itself
• 1