The GCF of two numbers is 850. Neither number is divisible by the other. What is the smallest that these two numbers could be?
That looks right to me, and those two numbers are not divisible either so good job.
What have you tried?
well, I'm not sure, but this is what I thought was right.
1700= 2x2x5x5x17
2550= 2x3x5x5x17
GCF= 2x5x5x17= 850
To find the smallest possible values for the two numbers with a greatest common factor (GCF) of 850, we need to understand the properties of the GCF.
The GCF is the largest positive integer that divides two numbers without leaving a remainder. In this case, the GCF is given as 850, which means both numbers are divisible by 850.
Since neither number is divisible by the other, we can consider any common factors they might have. In order for the GCF to be 850, these common factors should be multiplied by some other factors to get back to the original numbers.
To find the smallest numbers with a GCF of 850, let's list down all the factors of 850:
Factors of 850: 1, 2, 5, 10, 17, 34, 50, 85, 170, 425, 850
Since neither number can be divisible by the other, we need to pair up these factors such that none of the pairs multiply together to give a product of 850.
We start pairing from the smallest and largest factors:
1 x 850 = 850 (not valid since 850 is divisible by 850)
2 x 425 = 850 (valid)
5 x 170 = 850 (valid)
10 x 85 = 850 (valid)
12, 15, 17, 34, 50, and 85 can't be paired with any of the other factors without resulting in a product of 850.
From the valid pairs, we can see that the smallest numbers are 2 and 425. These numbers have a GCF of 850, and neither is divisible by the other.
Therefore, the smallest possible values for the two numbers are 2 and 425.