stumbling

What is the greatest common divisor of all of the members of the set containing all numbers that are the product of four consecutive positive integers?

 

With any four consecutive numbers there will always be 2 even ones and one of those will be divisable by 4.

So that means that 8 will always be a factor of their product.

Also there will always be one that is divisable by 3 so there is another common factor.

So 24 will be a common factor.

 

Now the smallest member of the set is  1*2*3*4= 24

 

So 24 is the greatest common factor.

GCD[Greatest Common Divisor] of ANY four consecutive positive integers will always be a 1.

GCD[1, 2, 3, 4] =1, GCD[2, 3, 4, 5]=1, GCD[22, 23, 24, 25]=1, GCD[171, 172, 173, 174]=1.......and so on.