I just think about algorithm to find factor of number by doing something like guessing last digit of number and increase digit bit by bit
Such as, I want to find factor of 749
Algorithm would begin guessing that only 3*3 and 7*7 can result in last digit 9
Then it would increase next digit. To find that only 83*03 and 07*07 result in last two digit 49 (43*43 also give 49 but it more than 749)
Then I would found only 107*007 is result factor of 749
Are there any name for this algorithm?
Your algirithm fails for a number like $19\cdot 31$, because it doesnt include the possibility that the last digit $9$ is obtained from $1\cdot 9$.
Even though the last digit is obtained from $m\cdot 1$, that doesn't mean that either of the factors will be equal to $1$. It just means one of the factors will end in a $1$.