Download Study Guide II

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Vocabulary
1. greatest common factor - largest common factor shared by two numbers
2. least common multiple - smallest common multiple shared by two numbers
3. simplest form - when the numerator & denominator of a fraction have no common factors except for 1
Determining the Greatest Common Factor (GCF)
OPTION 1: Listing Factors
Find the GCF for 12 & 36.
Step 1: Write all the factors (numbers) when multiplied together equal the starting number.
►factors of 12: 1, 2, 3, 4, 6, 12
►factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 2: Circle the common factors appearing in both lists.
►common factors: 1, 2, 3, 4, 6, 12
Step 3: Determine the GCF.
►12 is the greatest of the common factors
OPTION 2: Using Factor Trees & Prime Numbers
Find the GCF for 12 & 36.
Step 1: Create a factor tree for both numbers until only prime numbers remain.
12
36
3 x 4
6x 6
3 x 2 x 2
3x 2x 3x 2
Step 2: Circle all occurrences of the common prime numbers in the final line.
►common prime numbers are 3, 2, 2
Step 3: Determine the GCF
►multiply the common prime numbers (3 x 2 x 2)
►12 is the GCF
Determining the Least Common Multiple (LCM)
Listing Multiples
Find the LCM for 3 & 12
Step 1: Write all the multiples for the given number through 12. Multiples are found by taking the
number and multiplying it by 1, then 2, then 3, etc., etc.
►multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144
►multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
Step 2: Circle the common multiples appearing in both lists.
►common multiples: 12, 24, 36
Step 3: Determine the LCM.
►12 is the smallest of the common multiples
Simplifying Fractions (simplest form or lowest terms)
OPTION 1: Dividing by the GCF
Simplify
12
20
Step 1: Determine the GCF by using one of the options from the front page.
►4 is the GCF
12
Step 2: Divide the numerator & denominator by 4 20 ÷ 4
3
►simplest form: 5
OPTION 2: Random Dividing By Common Factors
Simplify
16
28
Step 1: Choose a common factor of the numerator & denominator.
►possible common factors 2, 4
Step 2: Divide both the numerator & denominator by your chosen common factor.
►Let’s try dividing by the common factor 2. 16
8
28 ÷ 2 14
Step 3: Ask yourself, “Is this fraction in simplest form?” In other words, can the numerator and
denominator be divided by a common factor other than 1?
►Yes, it can!
►Keep dividing by common factors until the numerator & denominator have no common factors
except for 1.
4
or simplest form.
►Eventually, you should get to
7
This method requires a strong knowledge of your basic facts!