Question

When 20 is divided by a positive integer n, the remainder is 2. How many possible values are there for n?

Answer 1

well n has to be less than 20 and not a factor of 20. so that rules out 1, 2, 4, 5, 10 and 20

Answer 2

a little confused still?

Answer 3

i am confused

Answer 4

well if n is larger than 20 the remainder will always be 20....

e.g 20/21 remainder 20 20/35 r = 20....

if n is a factor there is no remainder

Answer 5

we can try them all
20 divided by 18 leaves a remainder of 2

Answer 6

likewise 9

Answer 7

also perhaps 6

Answer 8

likewise 3

Answer 9

lol

Answer 10

think we got them all?

Answer 11

Let 20 = nk + 2 where k is an integer.

18= nk

18/n = k

So n would have to be a factor of 18.

Answer 12

n could be 1, 2, 3, 6, 9, 18 (total of 6) but should we exclude 18?

Answer 13

Oh, I see where you guys are getting at. Thanks! :)

Answer 14

20/n = x + 2/n = (nx + 2) /n
-> nx + 2 = 20
-> nx = 20 -2 = 18
The chance is: 1 * 18, 2 * 9, 3 * 6
Thus possible values of n = 1, 2, 3