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

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Homework Help Overview

The discussion revolves around finding the greatest common divisor (gcd) of the numbers 210 and 10!. The subject area includes number theory and factorials.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the Euclidean algorithm and express concerns about its efficiency. There is mention of seeking a "number trick" to simplify the process. Some participants suggest considering the prime factorization of 10! to determine the number of factors of 2.

Discussion Status

Participants are exploring different methods to approach the problem, including the potential of using prime factors. Some guidance has been offered regarding the significance of powers of 2 in the context of the gcd, but no consensus has been reached.

Contextual Notes

There is a mention of a desire to avoid a "guess and check process," indicating a preference for a more systematic approach to the problem.

lordy12
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large number!

1. Finding gcd(2^10,10!



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3. I attempted to try the Euclidean algorithm, but it would take forever. Is there a certain number trick?
 
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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?
 
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."
 
Then think of prime factors. How many 2's are there in the factorization of 10! ?
 
i got it. thanks
 

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