SOLUTION: How do you figure out the set of numbers when given the GCF? For example, the GCF of two numbers is 850. Neither number is divisible by the other. What is the smallest that these t

Question 13291: How do you figure out the set of numbers when given the GCF? For example, the GCF of two numbers is 850. Neither number is divisible by the other. What is the smallest that these two numbers could be? (This is for a 6th grade math class.) In addition, what guidelines apply when one number is even and the other odd, or both numbers are even/odd. I have been searching the net, but can only find out how to determine the GCF...not the other way around. Thank you!
Answer by greatscot(1) (Show Source):
You can put this solution on YOUR website!
Think of how you would find the GCF of the two numbers.
You would write each one as the product of prime factors like this.
Number one = 2 X 5 X 5 X 17 X m
Number two = 2 X 5 X 5 X 17 X n
2 X 5 X 5 X 17 occurs in both expressions because their product is 850, the GCF of the two numbers.
We get the numbers to be small by making m and n as small as possible. One of them will be 2 and the other will be 3. So the numbers are 850 X 2 = 1700 and 850 X 3 = 2550.