What is the last digit of 6 power 100

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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.

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 From the above table, we can see that for odd-odd combination last two digits will be Your email address will not be published. The stories that we are sharing here are some of those students whom we mentored right from the start of their preparation.

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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.

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. For larger exponents try the Large Exponents Calculator. For instructional purposes the solution is expanded when the base x and exponent n are small enough to fit on the screen.

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Another method is to expand the power using the Binomial theorem in such a way that many of the terms vanish mod Rudranil Ghosh says:. 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. April 7, at am. Example 3: what is the units digit in the expansion raised to 71? Submit your answer Find the last two digits of. Following the announcement of the change in pattern,. Please try again in a few seconds, and if the problem persists, send us an email. October 12, at am. Like Loading

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July 29, at am. Start the quiz! January 4, at pm. Here is a small quiz to test your understanding. CAT Online Course at affordable price. Then, by proving that this pattern holds often by induction , the last decimal digit of a power can be solved completely. The Chinese remainder theorem is a powerful tool to find the last few digits of a power. November 15, at pm. Main article: Modular Arithmetic The patterns of the previous section can be expressed elegantly in the language of modular arithmetic. In general, the last digit of a power in base n is its remainder upon division by n. Sign me up. After the second term, every term contains at least 2 zeros, and so they vanish mod Your email address will not be published. I am not sure who is right? Sign up.