"Remainder when 17 power 23 is divided by 16" is a bit challenging question for the people who are getting prepared for competitive exams.
Actually it is not a difficult question and it can be answered easily once we know the stuff.
Let us take exponents 0, 1, 2, 3, ....one by one to "17"
For example, if we take exponent "0" for 17, we get 17⁰ = 1
Here 1 is less than the divisor 16 and 1 can not be divided by 16.
If the dividend is less than the divisor, then that dividend itself to be considered as "Remainder"
So, if 17⁰ is divided by 16, we get the remainder "1"
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, 17⁰ is divided by 16, we get the remainder "1".
Again we get remainder "1" for the exponent "1".
Next we get remainder "1" for the exponent "2" and so on.
So, we get remainder "1", for all the exponents we take for 17.
Since we get the remainder 1 for all the exponents we take for 17,
when we divide 17²³ by 16, the remainder will be "1 ".
As soon as students have the questions like "Remainder when 17 power 23 is divided by 16" in competitive exams, they stumble a lot to answer. Even if they try to answer the questions like this, it takes more time.
Actually this kind of questions can be answered easily once they understand the concept.
After having gone through the stuff, we hope that the students would have understood "How to get remainder when 17 power 23 is divided by 16.
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