Question

(3 ki power 1989) is divided by 7, then remainder is:

Answer 1

The remainder will be 6.

When 3ˣ is divided by 7 the remainder can be any number from 1 to 6.

These remainder repeat themselves in a specific order.

For example,

3⁰/7 = 1/7, so remainder = 1

3¹/ 7 = 3/7, so remainder = 3

3²/7 = 9/7, so remainder = 2

3³/7 = 27/7, so remainder = 6

3⁴/7 = 81/7, so remainder = 4

3⁵/7 = 243/7, so remainder = 5

3⁶/7 = 729/7, so remainder = 1

3⁷/7 = 2187/7, so remainder = 3

Hence these remainder repeat itself at an interval of six.

Hence ,

Remainder of 3¹⁹⁸⁹ /7 = remainder of  (3³³¹*⁶ ⁺³)/7

= remainder of 3³/7

= 6

Hence the remainder of 3¹⁹⁸⁹/7 is 6.

Answer 2

Thank you for asking this question. The options for this question are missing. Here are the missing options:

A. 1

B. 5

C. 6

D. 4

E. 3

Answer:

3 / 7 remainder = 3

3^2 = 9 / 7 remainder = 2

3 ^ 3 = 27 / 7 remainder = 6 or -1 (equation 1)

1989/3 = 663

From the equation 1 above,

3 ^ 1989 = (3^3) ^ 663 ;

rem = (-1) ^ 663 = -1 or 6  

So the final answer for this question is Option C: 6

If there is any confusion please leave a comment below.