1.1 Factors and Multiples Lesson

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

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

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​You use the greatest common factor when simplifying fractions.

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​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.

​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

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

​2,3,5,7,11,13,17,19,23,.......

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

​4, 6, 8, 9, 10, 12, 14,.........

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​1 is neither prime or composite.

​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.

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

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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.

​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.

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.

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