What is the last digit of 6 power 100

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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 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.

What is the last digit of 6 power 100

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. So lets have a look at the technique to calculate the units digit of large numbers. One of the ways of finding the units digit of a power is by finding the remainder when that number is divided by Example 1 : What is the units digit of to the power of ? Example 3: what is the units digit in the expansion raised to 71? We hope that you now have a good idea on how to find the units digit of a number raised to power. Here is a small quiz to test your understanding. Start the quiz! I am really interested in knowing what happens to the units. Hi, Anything to zero power is 1. Any number whose units digit ends in 1 or 5, the power of that number will also end in 1 or 5 respectively.

Already have a WordPress. Skip to content How would we go about finding the last digit of very large numbers, such as?

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 induction , the last decimal digit of a power can be solved completely. For example, the last digit of various powers of 1 to 9 are:. The last digits of the powers of two repeat in a cycle of 2, 4, 8, 6.

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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 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.

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Previous Previous post: What is a Topological Space? Following the announcement of the change in pattern,. Master concepts like these Get started Learn more in our Number Theory course, built by experts for you. Share this: Twitter Facebook. Join Now. Comment Reblog Subscribe Subscribed. Like Like. Username says:. The Chinese remainder theorem is a powerful tool to find the last few digits of a power. Log in with Facebook Log in with Google Log in with email. Recommended Course Number Theory Explore the powers of divisibility, modular arithmetic, and infinity. Home Courses. If not, then please revisit the concept before moving ahead.

This is an online calculator for exponents. Calculate the power of large base integers and real numbers.

The prerequisite is to memorise the square of the first 25 natural numbers. How would we go about finding the last digit of very large numbers, such as? Much of CAT turned out to be as expected, both in terms of pattern and difficulty. Notice that after the second term every term contains at least 2 zeroes. Gajendran P says:. Rudranil Ghosh says:. October 5, at pm. 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. Abhishek says:. Many mathematical contests ask students to find the last digit or digits of a power. CAT success stories of our , and batches bodheeprep December 29, Here, it is not straight forward to calculate the units digit of these numbers. Already have an account?