Solving the GCD of 2^10 and 10!: A Number Trick?

[lordy12]

large number!

1. Finding gcd(2^10,10!

Homework 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