Question

When 17 is divided by k,where k is a positive integer less than 17,,the remainder is 3.What is the remainder when the sum of the possible values of k is divided by 17?

Answer 1

[AI-generated answer — Explain Bot]

To find the remainder when the sum of the possible values of k is divided by 17, we first need to find the possible values of k.

From the given information, we know that when 17 is divided by k, the remainder is 3. This can be represented as the equation 17 ≡ 3 (mod k), where "≡" denotes "is congruent to".

To solve this congruence equation, we can subtract 3 from both sides: 17 - 3 ≡ 0 (mod k), which simplifies to 14 ≡ 0 (mod k).

Now we need to find all the factors of 14 that are less than 17, as k has to be a positive integer less than 17.

The factors of 14 are 1, 2, 7, and 14 itself. However, we need to exclude 14 from the possible values of k, as it is not less than 17.

Hence, the possible values of k are 1, 2, and 7.

To find the remainder when the sum of these possible values of k is divided by 17, we add them together: 1 + 2 + 7 = 10.

Finally, we need to find the remainder of 10 divided by 17. Performing this calculation, we find that the remainder is 10.

Therefore, the remainder when the sum of the possible values of k is divided by 17 is 10.

Answer 2

k can be 14, or 7

Answer 3

the choices r

2
3
4
5
6