Newton's law of universal gravitation:
Gravitational Force, in Newtons, between two objects =
(a constant)·(one mass)·(the other mass)/(distance between them)²
acting on EACH object, in the direction of the other object.
If the masses are in kilograms and the distance is in meters, then the constant is 6.67 x 10⁻¹¹ m³/kg-sec² .
I may be wrong, but I don't think Newton had any number to use for the constant. It had not been measured yet, the kilogram and the meter had not been invented yet, and there certainly was no unit called "a Newton" during his lifetime.
He might have been able to calculate the value of the constant by applying his law of gravity to the motion of one or two planets. But he would have needed to know the mass of the sun and the planets he used, and I don't think those were known yet in Newton's time.