What is the last digit of 6 power 100

How would we go about finding the last digit of very large numbers, such as? A problem like this can be tackled by listing out the initial expansions of a power in order to determine a pattern. Then, by proving that this pattern holds often by inductionthe last decimal digit of a power can be solved completely.

We will first try to understand what is a units digit, then we will look at the technique to find the units digit of large powers and then using this technique we will solve some problems on Units digit of a number raised to power. At the end, please take the QUIZ to test your understanding. For example, the units digit of is 3, the units digit of 39 is 9. But then what is the units digit of large numbers like 23 to the power 46 or what is the units digit of to the power of ? Here, it is not straight forward to calculate the units digit of these numbers.

What is the last digit of 6 power 100

Last Two digits: The objective of this article is to understand the concept and approach to solve questions like:. There are two-three shortcut approaches to solve the above problems. But before we go and apply the same, we need to understand the following basic points. The prerequisite is to memorise the square of the first 25 natural numbers. Now, number 78 is close to and the deviation of 78 from is 22 From the above examples, we can deduce that the if the number is close to or 50, the last two digits of the square of the number is equal to the last two digits of the square of the deviation of the number from the base or 50 whichever the number if close to. Note: To verify the above result, we can use the concept of binomial expansion. I leave the same to the readers to do. The correct answers are 2, 9, and 6 respectively. I hope you got all right. If not, then please revisit the concept before moving ahead.

Convert the number by repeatedly squaring until we get the unit digit as 1, and then applying the trick of finding the last two digits of number with unit digit 1 as explained above. Another method is to expand the power using the Binomial theorem in such a way that many of the terms vanish mod One of the ways of finding the units digit of a power is by finding the remainder when that number is divided by

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In Quantitative aptitude questions ask to find the last digit and last two digits of a power or large expressions. In this article explained different types of tools to serve as shortcuts to finding the last digits of an expanded power. From the above table we can observe as follow. Examples — 1 : Find last digit of the number 3 So from the above table unit digit of given number is — 7. Examples — 2: Find last digit of the number Solution: Here power value is odd number. So last digit of the given number is 4. Example 3 : What is the last digit of the number 4 Solution: Here power value is even number.

What is the last digit of 6 power 100

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Get Details. Primitive Roots. October 9, at pm. Sign up Log in. Units digit of a number raised to power. The patterns of the previous section can be expressed elegantly in the language of modular arithmetic. December 27, at pm. There are two-three shortcut approaches to solve the above problems. January 4, at pm. Your email address will not be published. The last digits of various powers of an integer are given in the table below:.

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How would we go about finding the last digit of very large numbers, such as? Dividing by 4 we get with no remainder. Read More ». Nora Martinez says:. I leave the same to the readers to do. Submit your answer Find the last 4 digits of the decimal representation of. Submit your answer What are the last 3 digits of. Submit your answer Find the last two digits of. One of the ways of finding the units digit of a power is by finding the remainder when that number is divided by The patterns of the previous section can be expressed elegantly in the language of modular arithmetic. Submit your answer Find the last 6 digits in decimal representation of.