How can you find the greatest common factor of two numbers?

Question

Everly Taylor · Accepted Answer

Here are a couple of methods...

Method 1 Multiply the two numbers together after factoring them into prime factors and determining the common factor. For example, find the GCF of #56# and #84# as follows: #56 = 2 xx 2 xx 2 xx 7# #84 = 2 xx 2 xx 3 xx 7# #GCF(56, 84) = 2 xx 2 xx 7 = 28# #color(white)()# Method 2 If the remainder is zero, the smaller number was the GCF; if not, repeat with the smaller number and the remainder. Given two numbers, divide the larger by the smaller to find a quotient and remainder. Example: find the GCF of #112# and #70#: #112 / 70 = 1# with remainder #42# #70 / 42 = 1# with remainder #28# #42 / 28 = 1# with remainder #14# #28 / 14 = 2# with remainder #0# So #GCF(112, 70) = 14#

Levi Adams · Answer

undefined To find the greatest common factor (GCF) of two numbers, you can use several methods:

1. Prime Factorization Method:
   - Find the prime factorization of each number.
   - Identify the common prime factors and their smallest exponents.
   - Multiply these common prime factors together to find the GCF.

2. Listing Factors Method:
   - List all the factors of each number.
   - Identify the common factors shared by both numbers.
   - Determine the largest common factor among the shared factors.

3. Euclidean Algorithm:
   - Divide the larger number by the smaller number.
   - Replace the larger number with the remainder of the division.
   - Repeat the process until the remainder is 0.
   - The divisor in the last division step is the GCF of the original two numbers.

Choose the method that best suits your preference or the requirements of the problem you're solving.