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Foundations & Pre-Calculus 10
Factors & Multiples of Whole Numbers
Lesson Focus: To determine prime factors, greatest common factors, and least common multiples of whole
numbers.
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the prime factorization of a natural number is the number written as a product of its prime factors
natural numbers greater than 1 that are not prime are composite
every composite number can be expressed as a product of prime factors
we can use a factor tree to determine the prime factors of a number
use the divisibility rules to help you to decide which numbers to use
e.g. Write the prime factorization of each number.
1. 80
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2. 72
if the starting number is quite large, we can use a factor ladder to break down the number
e.g. Write the prime factorization of each number.
1. 324
2. 405
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to avoid confusing the multiplication symbol with the variable x, we will use a dot to represent the
multiplication operation
i.e. 12 = 2 · 2 · 3 or 22 · 3
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the greatest common factor (GCF)of two or more numbers is the greatest factor the numbers have in
common
we can determine the GCF of two or more numbers by:
1. write the prime factorization of each number
2. multiply together the factors that appear in each prime factorization
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e.g. Find the GCF of each pair of numbers.
1. 44 and 70
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2. 36 and 48
the least common multiple (LCM) of two or more numbers is the least number that is divisible by each
number
we can determine the LCM of two or more numbers by:
1. write the prime factorization of each number
2. determine the greatest power of each prime factor in any list
e.g. Find the LCM of each pair of numbers.
1. 12 and 30
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2. 16 and 18
we can solve problems that involve using the GCF and the LCM
e.g. Two ribbons are 24 cm and 42 cm long. Each ribbon is to be cut into equal pieces and all pieces must
have the same length that is a whole number of centimetres. What is the greatest possible length of
each piece?
e.g. Hamburger patties come in packages of 8 while buns come in packages of 6. What is the least number
of hamburgers that can be made with no patties or no buns left over?