This answer is in the context of numbers that are likely to crop up in school or graduate mathematics, not in cryptology or advanced research.
Complete factorisation of large numbers is tedious and may require a lot of false starts (if the next factor is quite large). So, for large numbers I would start with Euclid's algorithm (see link). All that is required for this process is subtraction. The problem of finding the GCF of two large numbers soon becomes that of finding the GCF of two very much smaller numbers. Although the method can be carried out to the end, I will often choose to switch to factorisation when the numbers are smaller: below 400, say, when all you need to know is the times tables to 20. Given all the divisibility rules, this is not as daunting as it may sound.
It doesn't matter what method you use, you need at least two numbers to find a GCF.
34
Methods aren't necessary. The only common factor (which makes it the GCF) of 16 and 35 is 1.
There are ways to find the GCF of set of numers; by the factor tree method and by the decomposition method. I know that these methods are the easy ways to get your GCF, but there is much, much more easier; it is the Euclidean Algorithm Method, you just divide the larger number in the 2 given numbers and divide the remainder to the dividend until there is no remainder. then the answer will be the first reainder. ENJOY SOLVING PROBLEMS.! and thanks for reading, I just want to share to you the method that I just discovered.! :D
gcf difference of two squares guess ad check/ box method
The GCF of 50 and 54 is 2. Use whatever method you wish.
listing method , factor tree
The gcf is 3.
It doesn't matter what method you use, you need at least two numbers to find a GCF.
gcf of 138 and 207 is 69.
The GCF is 6. That makes the LCM 42.
9
The GCF of 12 and 20 is 4.
756
Method of prime factorization is a good method to find GCF.P.F. of 68 = 2x2x17P.F. of 56 = 2x2x2x7It is clear that 2x2 is the greatest common factor.Therefore, GCF of 68 and 56 = 4.
You need at least two numbers to find a GCF, whichever method you use.
25