Question

plz help..
when 15 is divided by the positive integers k, the reminder is 3. for how many different values of k is this true?

1
2
3
4
5

Answer 1

i am studying for the sat and i need to know the simpliest and fastest way to do this type of problem

Answer 2

2

Answer 3

no it is 3 in my book

Answer 4

yes right 3

Answer 5

4 , 6 , 12

Answer 6

can u plz explain in a more clear way?

Answer 7

if u divide 15 by 4 , u will get answer 3 & reminder 3.

Answer 8

15 = nk + r


15 = nk + 3


15-3 = nk


12 = nk


nk = 12


So any number that is a factor of 12 will work. However, 2 does NOT work since 15/2 = 7 remainder 1.

Answer 9

if u divide 15 by 6 answer 2 & reminder 3

Answer 10

@jim_thompson5910 what is n ?

Answer 11

n is any integer

so if n = 2 and k = 6 for instance, then

nk = 12

2*6 = 12

12 = 12

Answer 12

To satisfy that equation, n has to be less than 12

Answer 13

i dont get how u formed ur equation 15 = nk + r

Answer 14

When you divide 15 by k, you get

15/k

This will give you a quotient n and some remainder r

So

15/k = n+r/k

which can be rearranged to

15 = nk + r

Answer 15

ok @jim_thompson5910 now i get it but
how do u find the answer from this equation ?

Answer 16

You're simply looking for numbers that are factors of 12

So just count the factors of 12. Exclude 1, 2, and 3 because they won't work here.

Answer 17

ok so how did u know that u have to exclude those numbers

Answer 18

@jim_thompson5910

Answer 19

because

15/1 = 15 remainder 0

15/2 = 7 remainder 2

15/3 = 5 remainder 0

Answer 20

but we want a remainder of 3

Answer 21

OH ok thanku so much

Answer 22

oops, made a typo

15/2 = 7 remainder 1

Answer 23

but it still doesn't work

Answer 24

ok