The greatest common factor is the greatest number that is a factor of two (or more) other numbers.
When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
The greatest common factor of two or more other numbers can be found using the step below:
Step 1: Write out the factors of each of the numbers given,
Step 2: Write out the common factors in the numbers given
Step 3: Write out the number that is the largest factor that is common to the factors of the given numbers.
The abbreviation of Greatest Common Factor is GCF.
For example, the GCF of 15 and 21 is 3, this is because 1 and 3 are common factors of both 15 and 21, and 3 is the greatest of them.
Using the steps above, the greatest common factor of 96 and 71 is as shown below:
Step 1: Write out the factors of the two given numbers
the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
71 is a prime number, so its factors are itself and 1. The factors of 71 are 1 and 71
Step 2: Write out the common factors in the numbers given
The common factor in 96 and 71 is 1
Step 3: Write out the number that is the largest factor that is common to the factors of the given numbers.
The largest common factor would now be 1.
Hence, the greatest common factor of 96 and 71 is 1