Here are two videos to help you understand how to show partial product multiplication on grid paper.
https://www.youtube.com/watch?v=mjYYbwuued0
https://learnzillion.com/lessons/24-solve-2-by-2-digit-multiplication-problems-using-area-model
Here are two videos that explains prime factorization
https://www.youtube.com/watch?v=9YOuETNDqik
https://www.youtube.com/watch?v=1fITTYsCnuU