correct answer is: d) \large\frac{2}{17}

Explanation

Here, the given integers are \large\frac{14}{17}\normalsize,\ 3\large\frac{1}{17}\normalsize,\large\frac{28}{34} .
Or, \large\frac{14}{17},\ \frac{52}{17},\ \frac{14}{17} _{[covert mixed to improper fraction]}
The formula we use to get the HCF of two or more fractions is:
\large\frac{The\ HCF\ of\ Numerator}{The\ LCM\ of\ Denominator}

Here, given numerators are 14,52 and 14.
\therefore The HCF of 14,52 and 14 is =2
And given denominators are 17,17 and 17.
\therefore The LCM of 17,17 and 17 are =17
So that, the HCF of \large\frac{14}{17}\normalsize,\ 3\large\frac{1}{17},\ \frac{28}{34} is =\large\frac{2}{17}
\therefore The greatest fraction is \large\frac{2}{17} .
Ans: \large\frac{2}{17} is the greatest fraction which is exactly divisible the giving integers \large\frac{14}{17}\normalsize,\ 3\frac{1}{17}\normalsize,\large\frac{28}{34} as quotients.

These particular math questions can also be asked in the following ways:

1. Finding the maximum fraction divisor for 14/17, 3 1/17, and 28/34 ensuring whole number results.
2. What is the largest fraction that evenly divides 14/17, 3 1/17, and 28/34 to produce whole numbers?
3. Determining the greatest common divisor fraction for 14/17, 3 1/17, and 28/34 to yield integer quotients.
4. Finding the maximum fraction dividing evenly into 14/17, 3 1/17, and 28/34 for integer outcomes.
5. What is the largest fraction that divides evenly into 14/17, 3 1/17, and 28/34, yielding whole number quotients?