### Instruction: What is the sum of the reciprocals of the natural-number factors of 6?### Response: To find the sum of the reciprocals of the factors of 6, I need to first list all the factors of 6.
The factors of 6 are 1, 2, 3, and 6.
The reciprocals of these factors are 1/1, 1/2, 1/3, and 1/6.
To add these fractions, I need to find a common denominator.
The least common multiple of 1, 2, 3, and 6 is 6.
So I can rewrite the fractions as 6/6, 3/6, 2/6, and 1/6.
Now I can add the numerators and keep the common denominator of 6.
The sum is (6 + 3 + 2 + 1)/6 = 12/6.
I can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor of 6.
The simplified fraction is 2/1, or just 2.