large number!!

[lordy12]

1. Finding gcd(2^10,10!



2. Relevant equations



3. I attempted to try the Euclidean algorithm, but it would take forever. Is there a certain number trick?

[Dick]

gcd(a,b) is the largest number that divides both a and b. It must be a power of 2. Why did I say that?

[lordy12]

i know its a power of 2, but you still have to use the euclidean algorithm. I don't want a "guess and check process."

[Dick]

Then think of prime factors. How many 2's are there in the factorization of 10! ?

[lordy12]

i got it. thanks