## Quarter Wit, Quarter Wisdom: Magic or Math - Part II

*Posted on on September 26, 2011*

Today we will continue from where we left our last post. In the last post, we discussed that of any two consecutive integers, one and only one of them will be even. Out of 20 and 21, only 20 is even. Since 2 is a factor of 20, it will not be a factor of 21. Does that make sense? Sure. Every second number will have 2 as a factor.

On the same lines, can both the consecutive numbers have 3 as a factor? Let’s take the same example – 20 and 21. 3 is a factor of 21. Can it be a factor of 20 as well? Do we even need to check? Since 21 is a multiple of 3, the previous multiple must be 3 places before (i.e., 18) and the next multiple of 3 must be 3 places ahead (i.e., 24).