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When we try to find the Greatest common factor (GCF) of two numbers , does it only involve prime factorization ?
Yes.Ok , so the same prime factorization is used to find the LCM too , right ?
You'll find that in an "algebra for intelligent students" textbook!Thanks for the information mfb , i am just trying to cover the algebra 1 for dummies book .
It doesn't have a method like this LCM(a, b)=a*b/GCD(a, b) mentioned in it .
It's still worth understanding why the two are related. The basic argument is:lol ok , first let me somehow finish this one book properly
But you don't need to know anything about prime factorizations to find the GCD; you can use Euclid's algorithm, which is very efficient.Yes. The GCF is a product of primes but is not usually a prime itself. Prime factorization of both numbers is the way to find out what the GCF is. If you have the prime factorization of both numbers, it is easy to calculate the GCF.
This is wrong. Euclid's very efficient algorithm for finding GCDs does not require doing anything at all with prime numbers.Yes. The GCF is a product of primes but is not usually a prime itself. Prime factorization of both numbers is the way to find out what the GCF is. If you have the prime factorization of both numbers, it is easy to calculate the GCF.
Yes, that has been mentioned in post 6 for example.But you don't need to know anything about prime factorizations to find the GCD; you can use Euclid's algorithm, which is very efficient.