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.

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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. From the above table, we can see that for odd-odd combination last two digits will be

Any number whose units digit ends in 1 or 5, the power of that number will also end in 1 or 5 respectively.

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. Dividing by 4 we get with no remainder. Hence the sequence of digits repeats times with no extra entries, so the last digit should be 6.

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.

What is the last digit of 6 power 100

This is an online calculator for exponents. Calculate the power of large base integers and real numbers. You can also calculate numbers to the power of large exponents less than , negative exponents, and real numbers or decimals for exponents.

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Note: To verify the above result, we can use the concept of binomial expansion. CAT Online Course at affordable price. At the end, please take the QUIZ to test your understanding. This is likely due to network issues. Submit your answer What are the last 3 digits of. I leave the same to the readers to do. How would we go about finding the last digit of very large numbers, such as? Solving these types of problems gives a down-to-earth introduction to these techniques of elementary number theory. Main article: Modular Arithmetic The patterns of the previous section can be expressed elegantly in the language of modular arithmetic. Here, it is not straight forward to calculate the units digit of these numbers. Finding the last digit of a number is the same as finding the remainder when this number is divided by Previous Previous post: What is a Topological Space? Like Loading I am not sure who is right?

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The prerequisite is to memorise the square of the first 25 natural numbers. March 4, at am. The stories that we are sharing here are some of those students whom we mentored right from the start of their preparation. Submit your answer Find the last 4 digits of the decimal representation of. September 17, at pm. Here is a small quiz to test your understanding. Sign up with Facebook or Sign up manually. Prakash says:. Just tell us who you are to view your results! Please try again in a few seconds, and if the problem persists, send us an email. New user? Example 3: what is the units digit in the expansion raised to 71? CAT success stories of our , and batches bodheeprep December 29, 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. Units digit of a number raised to power.