Question 172928: what is the "GCF" of the following:
16,22
18,26
15,25
30,75
15,30
72,108
24,60
36,80
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! I'll do the first few using a detailed process. You can do the rest.
IN order to find the Greatest Common factor, you need to find the prime factors that make up each term. Here is a tool to help you check your ability to find prime factor --> http://www.virtuescience.com/prime-factor-calculator.html
16 = 2*2*2*2
22 = 2* 11
Each has a common factor of 2 -- and nothing more. So the GCF = 2
18 = 2* 3 * 3
26 = 2* 13
Again, only 2 is common. GCF =2
Skipping down a bit
15 = 3 * 5
30 = 2 * 3 * 5
In this case, each one contains both a 3 and a 5. so the GCF = 3*5 = 15
Skipping to the last one
36 = 2 * 2 * 3 * 3
80 = 2 * 2 * 2 * 2 * 5
Both contain 2 * 2, so the GCF = 4
Get the process?
Now, you won't be able to use the calculator on a test. You need to get a prime factorization by hand.
I always look for even numbers. I divide by 2. If the resulting quotient is even, I divide by 2 again. Keep dividing by 2 until the result is odd.
Then try 3 (if the sum of the digits if a number is divisible by 3, then the number is also divisible by three)
Then do 5 (five is easy too. The ones digit is either 0 or 5)
Keep walking up the prime numbers
2, 3, 5, 7, 11, 13, 17, 19 ....
Then use hat URL to check yourself
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