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find the remainder when 2 256 is divided by 17. please sirs tell me the answer

find the remainder when 2256 is divided by 17.
please sirs tell me the answer
 

Grade:10

1 Answers

SR Roy
128 Points
3 years ago

Let us take exponents 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ....one by one to "2" 

For example, if we take exponent "3" for 2, we get 2³ = 8

Here 8 is less than the divisor 17 and 8 can not be divided by 17.  

If the dividend is less than the divisor, then that dividend itself to be considered as "Remainder" 

If the dividend is greater than the divisor, then we have to divide the dividend by the divisor and get remainder. 

Let us deal our problem in this way. 

 

2

2¹

2²

2³

2

2

2

2

2

2

Value 

1

2

4

8

16

32

64

128

256

512

Remainder

1

2

4

8

16

15

13

9

1

2

When we look at the above table carefully, 2⁰  is divided by 17, we get the remainder "1".

Again we get remainder "1" for power "8".

Next we will get remainder "1" for power "16. 

So, we get remainder "1", if the exponent is a multiple of "8".  

In 2²⁶, the exponent is 256.   

This is a multiple of 8. Because 256 = 8 x 32.  

Since the exponent 256 is a multiple of 8, when we divide 2²⁶ by 17, the remainder will be 1. 

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