What is the purpose of the universal gravitation constant in newton's law of universal gravitation

The formula for the force of gravity is

                 Force = G  m₁ m₂ / R² .

If the formula were     

                  Force = m₁ m₂ / R² ,  without any 'G',

then in SI units, a couple of 10-kilogram blocks, 1 meter apart,
would attract each other with forces of  100 newtons ... about
23 pounds !

And in English units, a couple of 12-pound bowling balls
1 foot apart would attract each other with forces of 144 pounds !

As I'm sure you've noticed, they don't.

The forces of gravity are proportional to the product of the masses
divided by the square of the distance, but they're not equal to that
expression.  In order to make an equation from a proportion, you
need a constant in there, and that's what 'G' is for.