Factors of a number, in short, are simply numbers that divide or multiply into another number with no remainder or more simply - a pure or whole division.
Multiples of a number are the numbers that can be made from multiplying a number like in the multiplication table i.e. 3,6,9 are multiples of 3.
I have changed the sources of the video here to introduce you to different terminology like Quotient which is the correct term for 'how many times'
Multiples
Factors