helping my daughter....the GCF of 2 numbers is 850. What is the smallest that these numbers could be (& neither is divisible by the other) ? Why?

Question

anonymous · Answer

Well, the answer is 2*850=1700 and 3*850=2550.

If they just wanted the smallest, it would be 850 and 850.  If they also need to be different, then 850 and 2*850=1700.  But 850 divides 1700.  So you need to step away from using 850 as one of the numbers, because every other number with 850 as a factor would be divisible by 850.  So, pick the next smallest, 2*850=1700.  Then you can pick 2550 as the other number because 1700 does not divide 2550.

If you remove the 850 from the problem, then the problem becomes finding the two smallest numbers that don't divide each other.  That's 2 and 3.  The original problem is just this one, scaled up by a factor of 850.

anonymous · Answer

Thank you so much.......didn't have this when I was at school