**Proof:**

- Suppose that
*abc*, which is equal to 100*a*+ 10*b*+*c*, is a multiple of 37. - Thus 10000
*a*+ 1000*b*+ 100*c*is a multiple of 37. (Multiply the previous number by 100.) - Thus 10
*a*+ 1000*b*+ 100*c*is a multiple of 37. (Subtract 9990*a*, which is 270*a*× 37.) - Thus 10
*a*+*b*+ 100*c*is a multiple of 37. (Subtract 999*b*, which is 27*b*× 37.) - Thus
*cab*is a multiple of 37.

The proof that *bca* is a multiple of 37 is similar.