Question

Remainder of 2^47/47 ?; Remainder of 2^47/47 ?

Answer 1

answer is 2 .

we can also solve this using multiplication in bit and pieces. please mark it brainliest it it helps

Answer 2

Answer:

Step-by-step explanation:The question can be solved in multiple ways.

Using Fermat's Theorem

We have to find out Rem [2^47/47]

As per Fermat's Theorem, [a^(p-1)/p] = 1 where p is a prime number and HCF(a,p) = 1

=> Rem [2^46 / 47] = 1

To find out Rem[2^47 / 7], we can split 2^47 as 2*2^46

=> Rem [2^47 / 47]

= Rem [2 * 2^46 / 47]

= Rem [2/47] * Rem [2^46 / 47]

= 2 * 1

= 2

Using Simplifying the Dividend

Rem [2^47 / 47]

= Rem [2^3 * 2^44 / 47]

= Rem [8 / 47] * Rem [ 2048^4 / 47]

= 8 * Rem [27^4 / 47]

= 8 * Rem [(-20)^4 / 47]

= 8 * Rem [ 160000 / 47]

= 8 * Rem [160 / 47] * Rem [1000 / 47]

= 8 * 19 * 13

= 1976

= Rem [1976 / 47]

= 2