Question

find remainder when 2^46 is divided by 47​

Answer 1

Answer:

Power Even number n divisible number is odd which is next number to the power..As Like this

When 2^2 divide by 3 means it gives remainder 1

Answer 2

Therefore the remainder when the given number 2⁴⁶ is divided by 47 is '48'.

Given:

The exponential number = 2⁴⁶

To Find:

The remainder when the given number 2⁴⁶ is divided by 47.

Solution:

The given question can be solved as shown below.

The given exponential number = 2⁴⁶

Let us see the powers of 2 which make the number greater than 47. because 47 divides the number.

⇒ 2⁶ = 64 → 64/47 = Remainder = 17

Let us divide the power as the multiple of '6'

⇒ 2⁴⁶ = ( 2⁶ )⁷ × 2⁴ = ( 64 )⁷ × 16

Now by the Negative Remainder theorem, Remainder should be multiplied individually.

⇒ 2⁴⁶/47 = [ ( 17 )⁷ × 16 ] (Remainders )

Now 17² = 289 ⇒ 289/47 = Remainder = 7

17 × 16 = 272 ⇒ Remainder = 37

Now  2⁴⁶/47 = [ ( 17 )⁷ × 16 ] / 47 = [ ( 17² )³ × 17 × 16 ]/47 = 7³ × 37 ( Remainders )

Now 7² = 49 ⇒ 49/47 = Remainder = 2

7 × 37 = 259 ⇒ 259/47 = 24

⇒ ( 7³ × 37 )/47 = ( 49 × 259 )/ 47 = 2 × 24 (Remainders ) = 48

Therefore the remainder when the given number 2⁴⁶ is divided by 47 is '48'.

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