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FINDING THE GREATEST COMMON FACTOR OF 2 OR 3 NUMBERS

Jump right to the exercises!

A couple examples are given below. For a complete discussion, read the text.

EXAMPLES:
Find the greatest common factor of 27 and 18:
Answer: 9
The idea:
The factors of  27  are (in increasing order): 1,3,9,27
The factors of  18  are: 1,2,3,6,9,18
The common factors of  27  and  18  (the numbers that appear in both lists) are: 1,3,9
The greatest common factor is: 9

Here's an efficient algorithm for finding the greatest common factor,
when there aren't too many numbers, and they aren't too big:

The process is illustrated by finding the greatest common factor of  18 ,  36 , and  90 :
  • Line up the numbers in a row. (See the purple rectangle at left.)
  • Find ANY number that goes into everything evenly (like  2 ).
  • Do the divisions, and write the results above the original numbers.
    In the example:  18  divided by  2  is  9 ,  36  divided by  2  is  18 , and so on.
  • Keep repeating the process, until there isn't any number (except  1 ) that goes into everything evenly.
  • Multiply the circled numbers together. This is the greatest common factor!
  • In the example,  gcf(18,36,90) = 2·3·3 = 18 .

Here are some other ways the algorithm might be applied.
Of course, you get the same answer any correct way that you do it!

 
Click on "new problem" to get started!


Find the greatest common factor of:
  

Put your answer here:


Click here or press "tab" to check your answer:


When you're ready to time yourself, use these buttons.
When you "end timing," you'll get a summary sheet of your results. Good luck!