Question

6+b/b is an integer number. find all possible integer values of b​

Answer 1

Step-by-step explanation:

(6+b)/b = x (= an integer number)

6 + b = bx (= still an integer number)

6 = bx - b = b(x - 1) (= still an integer number)

b = 6/(x - 1) (= still an integer number)

now for b to be integer, (x-1) must be a factor of 6 (6 must be divisible by x-1 with 0 remainder).

and integer includes negative numbers too.

the factors of 6 are therefore

1, 2, 3, 6, -1, -2, -3, -6

so, b can be 6/±1 = ±6

b can be 6/±2 = ±3

b can be 6/±3 = ±2

b can be 6/±6 = ±1

so, all possible values for b are also the listed factors of 6 :

-6, -3, -2, -1, 1, 2, 3, 6