Shave off Last Two

One can test if an integer $n$ is divisible by prime $101$ by subtracting the last two digits (as a number) from $n$ with those digits shaved off, and see if the result is divisible by $101$. For example, $162794931$ is divisible by $101$ because $1627949 - 31 = 1627918$ and $101 \, | \, 1627918$.

What are the smallest factors you should multiply the last two digits of $n$ (as a number) with, before subtracting from the shaved-off $n$ in the divisibility tests for $p = 43$ and $p = 67?$

Give your answer as the product of the factors.