Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.

The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:When the "r" is the greatest common divisor for the two fractions. So, we will use Euclid's algorithm:   [tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex] this is  [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex] we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0.  Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]". Learn more:greatest rational number:brainly.com/question/16660879