To find the greatest common factor (GCF) you can use one of a few methods. One way (which i think is the hardest) you list all the factors of those two numbers. Another way is to just multiply the numbers together. Now, if you have big numbers, these steps might be a little complicated or harder to do, but if you want to list all the factors of that number, go right ahead.
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Yes there is
The GCF is 8.
The GCF is 25.
The GCF is 3.
Nobody. That is because there is no pattern to prime numbers. There are various methods to find some classes of prime numbers but none that will find all of them.