Download worksheet 1 Review of Grade 9 GCF LCM File

Unit 2: Roots & Powers
Math 1201
GCF & LCM
Definitions to Remember:
1. Factors
• Numbers or algebraic expressions that multiply to get a product are
factors of that product
• Any number that divides evenly into another number is a factor of
that number
• Ex. 5 × 7 = 35 so 5 and 7 are factors of 35
• Ex. 45 ÷ 9 = 5 so 9 is a factor of 45
2. Prime Number
• A whole number with exactly two factors, itself and 1.
• Ex. 2, 3, 5, 7, 11, 13 are the first 6 prime numbers
3. Composite Number
• A number with three or more factors
• Ex. 8 is a composite number because its factors are 1, 2, 4, 8
4. Prime Factor
• A prime number that is a factor of another number
• Ex. 5 is a prime factor of 30
5. Prime Factorization
• Writing a number as a product of its prime factors
• Ex the prime factorization of 20 is 2 × 2 × 5 or 22 × 5
6. Factor Tree
• A branching diagram with a number at the top and its prime factors at
the bottom
• Created by continually factoring the numbers until no more factors
can be made because all the numbers are prime
• Ex. A factor tree for 3300
3300 = 22 × 3 × 52 × 11
7. Greatest Common Factor : GCF
• The highest number that divides evenly into each number is a given
set of numbers
• Ex. 5 is the GCF of 10 and 15
8. Least Common Multiple (or Lowest Common Multiple) : LCM
• The smallest number that two or more given numbers will divide
evenly into
• Ex. The LCM of 8 and 12 is 24
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Unit 2: Roots & Powers
Math 1201
GCF & LCM
Two Methods to Find the GCF
Two Methods to Find the LCM
1. Listing
1. Listing
• List the factors of the given numbers • List the multiples of the given
numbers
• The highest number that appears in • The lowest number that appears in
all lists is the GCF
all lists is the LCM
2. Factor Trees
2. Factor Trees
• Make a factor tree to write the prime • Make a factor tree to write the prime
factorization of each number
factorization of each number
• Take the product of the lowest
• take the product of highest power
power of each common prime factor
of each prime factor
that appears in all lists
Ex 1. Find the GCF of 138 and 198
Ex 2. Find the LCM of 18, 20 and 30
Determine the GCF of 126 and 144
Determine the LCM of 28, 42 and 63
Textbook Page: 140: 5. a, b; #6. a, b; #8 a; #9. a; #10 a; #11 a, #13, #17,
#19a
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