Question

Find the remainder when 2^{179} is divided by 7?
Select one:
a. 1
b. 3
c. 2
d. 4

Answer 1

Given :  2^{179}   is divided by 7 ,  2¹⁷⁹/7

To find : Remainder

Solution:

2¹⁷⁹

=  2² * 2¹⁷⁷

= 4 * ( 2³ˣ⁵⁹)

= 4 * (2³)⁵⁹

= 4 *  (8)⁵⁹

= 4 *  (7 + 1)⁵⁹

(7 + 1)⁵⁹  will have all terms  with  7 except   last term with 1

hence remainder will be  1  when (8)⁵⁹ is Divided by 7

there is a multiplier of 4  with  (8)⁵⁹

Hence remainder = 4 * 1  = 4

remainder = 4   when 2¹⁷⁹  Divided by 7

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