This worksheet explores prime factorization to discover the GCF of two numbers. It includes a demonstration and six different sets of numbers for students to put their learning into action and understand the concept further.

To find the greatest common factor (GCF) using prime factorization, a student can start by breaking down each number into its prime factors, which are prime numbers that multiply together to give the original number. For example, for the numbers 12 and 18, they would first find that 12 can be written as 2 x 2 x 3, and 18 can be written as 2 x 3 x 3. Next, they identify the common prime factors between both sets of prime factors. Here, both 12 and 18 share the prime factors 2 and 3. Finally, they multiply these shared prime factors: 2 x 3 = 6. Hence, the greatest common factor of 12 and 18 is 6. By focusing on the prime numbers common to each set, they can find the GCF.