One can test if an integer is divisible by prime by subtracting the last two digits (as a number) from with those digits shaved off, and see if the result is divisible by . For example, is divisible by because and .
What are the smallest factors you should multiply the last two digits of (as a number) with, before subtracting from the shaved-off in the divisibility tests for and
Give your answer as the product of the factors.