Well, this is a simple, basic and I think even silly doubt. The first time I saw the definition of momentum as $p = mv$ I started to think why this is a good definition. So I've read the beginning of Newton's Principia where he said that momentum is a measure of quantity of motion.
Well, this started to make sense: if there's more mass, there's more matter and so there's more movement going on. If also there's more velocity, the movement is greater. So it makes real sense that quantity of motion should be proportional both to mass and velocity.
The only one thing I've failed to grasp is: why the proportionality constant should be $1$? What's the reasoning behind setting $p = mv$ instead of $p = kmv$ for some constant $k$?
Thanks in advance. And really sorry if this doubt is to silly and basic to be posted here.