GCF and LCM of any pair
Both numbers, both ways of getting them, and the identity that ties them together: the greatest common factor times the least common multiple equals the two numbers multiplied, always. Every page here prints that check, so the answer proves itself.
Division and factors both
The Euclidean algorithm line by line, and the same answer built from the shared primes. Two routes to one number is how you know it is right.
Coprime is an answer
A GCF of 1 is not a failure to find one. It means the LCM is the plain product, and a fraction of those two will not reduce at all.
One gives you the other
Because the product is fixed, you never need to compute both: divide the numbers multiplied by whichever you have.
The pairs people ask for
By number
All 541 pairs, grouped by the number they contain. Each page lists what that number shares a factor with and what it shares nothing with.
Any numbers at all
The GCF and LCM calculator takes up to three numbers of any size, and the factor calculator lists every divisor of one.