REMAINDER WHEN 2 POWER 256 IS DIVIDED BY 17

In this section, you will learn how to find remainder when 2 power 256 is divided by 17. 

Let us take exponents 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ....one by one for '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 the dividend itself has to be considered as 'Remainder'.  

So, when 2³ is divided by 17, the remainder is 8.

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. 

When we look at the above table carefully, 2⁰  is divided by 17 and the remainder is 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 of 2 is a multiple of 8.  

In 2²⁵⁶, the exponent is 256.   

This is a multiple of 8. Because

256  =  8 x 32

Because 256 is a multiple of 8, when we divide 2²⁵⁶ by 17, the remainder will be 1. 

What if the exponent is not a multiple of 8? 

Let assume an exponent which is not a multiple of 8.

For example, say the exponent is 263.

What will be the remainder, if 2²⁶³ is divided by 17

The exponent 263 is not a multiple of 8.

Write 263 in terms of multiple of 8 using division algorithm.

263  =  8 x 32 + 7

or

263  =  256 + 7

Then, 

2²⁶³  =  2^{256 + 7}

2²⁶³  =  2²⁵⁶ x 2⁷

In 2²⁵⁶, the exponent 256 is a multiple of 8.

As explained in the above picture, using division algorithm, we can write 2²⁵⁶ as 

2²⁵⁶  =  17k + 1

Then, 

2²⁶³  =  2²⁵⁶ x 2⁷

2²⁶³  =  (17k + 1) x 2⁷

2²⁶³  =  (17k + 1) x 128

Now we can get the remainder when 2²⁶³ divided by 17 as given below. 

Therefore, the remainder is 9 when 2²⁶³ is divided by 17.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6