Transcript Using Prime Factorizations:

Using Prime Factorizations:
How can prime factorizations help
us find the GCF and LCM of two
numbers????
Prime Factorization Defn:
• The prime factorization of a number is a
string of factors made up of only prime
numbers.
The GCF:
• Find the Prime Factorization of 24 and 60.
• 24 =
and 60 =
• Work with your partner:
• What would be the GCF of 24 and 60?
• The GCF would be the product of the
longest string of prime factors that the
numbers have in common. For example,
the longest string of factors 24 and 60
have in common is 2 x 2 x 3.
So, the GCF of 24 and 60 is : 2 x 2 x 3 = 12
Now you try….
• Using the idea of prime factorization, find
the GCF for:
• 48 and 72
• 30 and 54
The LCM:
• 24 = 2 x 2 x 2 x 3 and 60 = 2 x 2 x 3 x 5
• Work with your partner to come up with a
way to find the LCM of 24 and 60 using
their prime factorizations.
• The least common multiple of two
numbers is the product of the shortest
string that contains the prime
factorizations of BOTH numbers.
• For example: the shortest string that
contains the prime factorizations of 24 and
60 is: 2 x 2 x 2 x 3 x 5
Now you try….
• Find the least common multiple for:
• 48 and 72
• 30 and 54
Follow-up:
• The GCF of 25 and 12 is 1. Find two other
pairs of numbers with a GCF of 1. Such
pairs of numbers are said to be relatively
prime.
• The LCM of 6 and 5 is 30. Find two other
pairs of numbers for which the LCM is the
product of the numbers.
• Find two pairs of numbers for which the
LCM is small than the product of the two
numbers. For example, the product of 6
and 8 is 48; the LCM is 24.
• How can you tell from the prime
factorization whether the LCM of two
numbers is the product of the two numbers
or is less than the product of the two
numbers? EXPLAIN