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In order to understand the concepts of Greatest Common Factor (GCF) and Least Common Multiple (LCM), we need to define two key terms: Multiple and Factor

Multiple: Multiples of a number are the result of multiplying that number by some other whole number.

Factor: Factors are the numbers you multiply to get
another number. For example: the factors of 21 are 3 and 7 because 3 x 7 = 21. Factor: A factor of a number will also divide that number evenly, with no remainder. 3 is a factor of 15 because 15 ¸ 3 = 5 exactly (with no remainder)

Greatest Common Factor
The Greatest Common Factor (GCF) of two or more numbers is the product of all the factors they share in common. In order to find the factors they share in common, we use something called prime factorization to find the number’s factors. We can find a number’s factors 2 different ways. 1) Factor tree 2) U table

Circle your prime factors (in this example 2, 2, and 3).
Factor Tree Prime factorization (or finding primes factors) can be done using a factor tree. Circle your prime factors (in this example 2, 2, and 3). The prime factorization of 12 = or 12 = Remember a means MULTIPLY! 2

Factors come in a pair of 2 numbers. Example: 1 x 2 = 2 2 x 2 = 4
U table Factors come in a pair of 2 numbers. Example: 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 To make sure we do not miss any factor pairs we should use a U table when solving for GCF problems. Whatever # we are solving for goes on the top List the factors starting with 1 List the factor paired with 1 Once the last two numbers in your table Meet you know you have found all the factors.

Prime Numbers Prime #: is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words… a prime number is any number whose only factors are 1 and itself. Example: 2, 3, 5, 7, 11, 13, 17…

Composite Numbers Composite #: a positive integer that has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.

PRIME COMPOSITE

GCF Practice: What are the factors of 12 and 8?
What are the COMMON factors of 12 and 8? What is the GREATEST of all the common factors? 12 8

LCM Practice: What are the first 6 multiples of 12? 12:
8: What is the LEAST (smallest) common multiple?