Greatest number dividing 37, 66, 89 with remainders

The required number is the $\text{HCF}$ of $(37 - 2)$, $(66 - 3)$, and $(89 - 5)$. Numbers are 35, 63, 84. $35 = 5 \times 7$ $63 = 3^2 \times 7$ $84 = 2^2 \times 3 \times 7$ $\text{HCF}(35, 63, 84) = 7$.