When 15 is divided by y, the remainder is y - 3. If y must be an integer, what are all the possible values of y?
i.e. 15/y = k + (y-3)/y , where k is a non negative integer.
i.e. 15 = ky + (y-3)
i.e. 15 = (k+1)y - 3
i.e. 18 = (k+1)*y = Positive Integer * Positive Integer
Let us try to represent the number 18 as a product of two different positive integers.
18 = 18*1 = (k+1)*y. So, k = 17 and y = 1.
18 = 9*2 = (k+1)*y. So, k = 8 and y = 2.
18 = 6*3 = (k+1)*y. So, k = 5 and y = 3.
18 = 3*6 = (k+1)*y. So, k = 2 and y = 6.
18 = 2*9 = (k+1)*y. So, k = 1 and y = 9.
18 = 1*18 = (k+1)*y. So, k = 0 and y = 18.
We, now, know that y can be 1,2,3,6,9,or 18. But y-3 is the remainder and the remainder is always non-negative. i.e. y-3>0. i.e y>3. y = 1,2 can be eliminated and we are left with 3,6,9,18
