1.1 Factors and Multiples Lesson

1.1 Factors and Multiples Lesson

Vocabulary

​Greatest Common Factor (GCF)

Common Factor: a factor shared by two or more numbers.​

Greatest Common Factor: The greatest or largest factor of two or more numbers.

​

​You use the greatest common factor when simplifying fractions.

​

​Three Ways to Find:

• ​Listing the factors of each number and finding the largest factor they have in common.

• ​Making a factor tree and multiplying the common factors in both.

• ​Ladder Method to find the GCF and LCM.

​Listing Factors

​Trick: If you are finding the GCF you can just list the factors of the smallest number because you will not have a common factor any larger than the smallest number because it needs to be in common with the other numbers

Multiple Choice

Find the GCF for

12 and 66

• 12

• 66

• 6

• 3

Multiple Choice

Find the GCF for

18 and 30

• 18

• 6

• 30

• 3

​Vocabulary

​Prime Number: a number that only has two factors one and itself.

​2,3,5,7,11,13,17,19,23,.......

​

​Composite Number: a number that has more than two factors.

​4, 6, 8, 9, 10, 12, 14,.........

​

​1 is neither prime or composite.

Least Common Multiple (LCM)

​Multiple: the product of a number and any other number. The multiples of 5: 5,10,15,20,25,30.......... Think MULTIPLY!!!!!

​Common Multiple: a multiple shared by two or more numbers.

​Least Common Multiple (LCM): the smallest common multiple share by two or more numbers.

​

You use the Least Common Multiple when adding and subtracting fractions.

​

Three Ways to Find LCM:

• ​Listing the multiples of each number and finding the largest factor they have in common.

• ​Making a factor tree and multiplying all the factors in both numbers.

• ​Ladder Method to find the GCF and LCM.

​Listing Multiples

​Trick: If you are finding the LCM you can just list the factors of the largest number because you will not have a common factor any smaller than the largest number because it needs to be in common with the other numbers.

Multiple Choice

Find the least common multiple (LCM) of

2 and 6

• 2

• 3

• 6

• 12

Multiple Choice

Find the least common multiple (LCM) of

4, 5 and 10

• 4

• 5

• 10

• 20

​Ladder Method to find GCF and LCM

1. ​Write the numbers side by side with an L around it.

2. ​Write the smallest prime number that goes into Both numbers evenly on the left side of the L.

3. ​Divide the numbers inside the L by the prime number and write the quotients under the numbers.

4. ​Repeat until nothing goes into Both of the quotients evenly.

5. ​Use the numbers on the outside of the L to help find the LCM and GCF.

   1. LCM: Multiply all the numbers outside to the left and below the L. (All around the L.)

   2. GCF: Multiply all the numbers on the outside LEFT of the L.

Multiple Choice

Find the LCM and GCF for 3,9 and 15

• GCF: 45

  LCM: 3

• GCF: 3

  LCM: 45

​Using LCM for Real Life Problem

​Use the LCM to find when they will meet again.