Find the largest prime factor of 451^2-137^2 without using a calculator.

451^2 - 137^2  =

( 451 - 137) (451 + 137)  =

( 314) ( 588 )

[ 157 * 2 ]  [ 294 * 2 ]

[ 157 * 2 ] [ 147 * 2 * 2 ]

[ 157 * 2 ]  [ 49 * 3 * 2 * 2 ]

[ 157 * 2 ] [  7 * 7 * 3 * 2 * 2 ]

157 * 7^2 * 2^3 * 3

So.....157 is the largest prme factor