Question

How do you find the GCF of a set of numbers? Think of two or three ways.

A) Prime factorization
B) Long division
C) Subtraction method
D) All of the above

Answer 1

There are multiple methods to find the GCF, including prime factorization, long division, and the subtraction method. Prime factorization involves identifying the common prime factors, while the subtraction method requires subtracting the smaller number from the larger until both numbers are equal.

Step-by-step explanation:

To find the Greatest Common Factor (GCF) of a set of numbers, one can employ several methods. Some of the proven techniques include:

• Prime factorization: Break down each number into its prime factors and multiply the common factors.
  
• Long division: Using the division method, divide the larger number by the smaller one and find the highest number that divides both without a remainder.
  
• Subtraction method: Repeatedly subtract the smaller number from the larger one until both numbers equal each other; that number is the GCF.
  

All of these methods (A, B, and C) are valid ways to find the GCF.

When using the prime factorization method, begin by dividing the number by the lowest prime until you reach 1. Do this for each number in your set, then identify the common factors in all lists and multiply them together for the GCF. In contrast, the subtraction method involves subtracting the smaller number from the larger until they are equal, and the result is the GCF. This method might take longer for large numbers but is simple to understand.