Largest possible common difference of an arithmetic progression given its three terms (not necessarily adjacent)

Question

How can I find the largest possible common difference of an arithmetic progression given that its three terms (not necessarily adjacent) are $0.37$, $9$ and $\frac{71}{7}$?

Answer 1

The common difference must divide the difference of any two terms of an AP. So it must divide $9-0.37=863/100$ and $71/7-9=8/7$. You want the largest common difference, i.e. the HCF of $8.63$ and $8/7$. Now use the following link: Rational Numbers - LCM and HCF.