Let p=2n+1 for n=10, 20, 30, or 40. For which value of n does p2−1 have the most factors?

For n= 40 p has 7 factors

For n= 20 p has 7 factors

For n= 10 p has 6 factors

For n= 30 p has 6 factors

Step-by-step explanation:

p = 2n + 1

Putting the value of n= 10

p1= 20+1= 21

Putting the value of n= 20

p2= 40+1= 41

Putting the value of n= 30

p3= 60+1= 61

Putting the value of n= 40

p4= 80+1= 81

p2- 1= (p+1)(p-1)

         = (81+1)(81-1)

         =( 82)(80)

          = 6560

             = (1312)5

             = 328)4)5

             = 41 (2)(2)(2)(2)(2)(5)

p2- 1= (p+1)(p-1)

         = (61+1)(61-1)

          =( 62)(60)

          =3720

            = (465)(8)

            = (93)(5)(8)

             = (31)(3)(5)(2)(2)(2)

p2- 1= (p+1)(p-1)

         = (41+1)(41-1)

          =( 42)(40)

          = 1680

           = (7)(3)(5*2)(2*2*2)

p2- 1= (p+1)(p-1)

         = (21+1)(21-1)

         =( 22)(20)

         = 440

         = (11)(2)(5)(2)(2)