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

Forgot password? New user? Sign up. Existing user? Log in. Already have an account? Log in here. Many mathematical contests ask students to find the last digit or digits of a power. However, there are a number of tools, such as modular arithmetic , the Chinese remainder theorem , and Euler's theorem that serve as shortcuts to finding the last digits of an expanded power. Solving these types of problems gives a down-to-earth introduction to these techniques of elementary number theory. A common way to attack these type of questions is to list out the initial expansions of a power to determine a pattern. Questions which ask about the last decimal digit of a power can be solved completely after proving that the pattern in question holds often by induction. The last digits of various powers of an integer are given in the table below:.

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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

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What is the last digit of 6 power 100

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

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Leave a comment Cancel reply. Log in with Facebook Log in with Google Log in with email. Rakesh Vishwakarma 27 Comments. Not only was there a change in exam pattern but also the difficulty level of almost. The Chinese remainder theorem is a powerful tool to find the last few digits of a power. Shahil Raza says:. June 1, at pm. If not, then please revisit the concept before moving ahead. Recommended Course Number Theory Explore the powers of divisibility, modular arithmetic, and infinity. Submit your answer What are the last 3 digits of.

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Username says:. Share this: Twitter Facebook. Notice that after the second term every term contains at least 2 zeroes. CAT Online Course at affordable price. Your email address will not be published. Fatima Raza says:. We can use this fact to decompose the congruence into easier ones:. Gajendran P says:. Shahil Raza says:. Parveen says:. New user? CAT Online Courses. September 17, at pm. Nora Martinez says:. Primitive Roots.