Factors

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Factors

• Greatest Common Factor Least Common Multiple

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Factor

• Factors are natural numbers you can multiply
  together to get another number.
• Example 3 4 12, so 3 and 4 are factors of 12

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Factors

• Every number has at least two factors
• What are those two factors every number has?
• Prime
• Composite -

Any number that has only 1 and itself as a factor.
A number in which it has more factors other than
1 and itself.
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Greatest Common Factor

• abbreviated GCF
• definition the largest natural number that is a
  factor of all numbers in a group
• examples 18 is the GCF of 36 and 54
• 1 is the GCF of 7, 13, and 21

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How To Find GCF LCM

• There are two ways to find the GCF and LCM
• Listing Factors/Multiples Method
• Prime Factorization Method

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Least Common Multiple

• abbreviation LCM
• definition the smallest natural number that is
  a multiple of all the number in the group (i.e.
  the smallest number that all the numbers go into)
• examples 30 is the LCM of 15 and 10
• 25 is the LCM of 5 and 25

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Listing Factors/Multiples

• Find the GCF and LCM of 12 and 18

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Finding the GCF

1. Write the prime factorization of each number
2. Choose all primes common to all factorizations,
   with each prime raised to the least exponent that
   it has in any factorization
3. Find the product of all the numbers. This is your
   GCF

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Example

• Find the GCF of 1800 and 21000.

Step 1 Find the prime factorization of each
number. 1800 23 32 52 21000 23 3 53
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Step 2 Find all primes in common and raise them
to the lowest exponent. 1800 23 32
52 21000 23 3 53 7
Step 3 Find the product. 23 3 52 600 The
GCF of 1800 and 21000 is 600
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Find the GCF.

1. 12, 18, 60
2. 90, 168

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Finding the LCM

1. Write the prime factorization of each number
2. Choose all primes belonging to any factorization,
   with each prime raised to the largest exponent
   that it has in any factorization
3. Find the product of all the number. This is your
   LCM

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Example

• Find the LCM of 24 and 38.

Step 1 Find the prime factorization of each
number. 24 23 3 38 2 19
Step 2 Find all primes raised to the highest
power. 24 23 3 38 2 19
Step 3 Find the product. 23 3 19 456 The
LCM of 24 and 38 is 456
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Find the LCM.

1. 12, 18, 60
2. 90, 168

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Trick for LCM of 2 Numbers

• This formula will only work for a pair of natural
  numbers
• LCM (mn)/GCF(m and n),
• where m and n are any natural number

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Find the LCM using the formula

1. 45 and 75
2. 84 and 180

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Homework

• Worksheet 1 - 15