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. 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

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.

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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

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.

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.

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If not, then please revisit the concept before moving ahead. The prerequisite is to memorise the square of the first 25 natural numbers. Log in now. The patterns of the previous section can be expressed elegantly in the language of modular arithmetic. Not only was there a change in exam pattern but also the difficulty level of almost. Solving these types of problems gives a down-to-earth introduction to these techniques of elementary number theory. From the above table, we can see that for odd-odd combination last two digits will be So lets have a look at the technique to calculate the units digit of large numbers. Following the announcement of the change in pattern,. Like Loading August 24, at am. Sign up Log in.

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.

Master concepts like these Get started Learn more in our Number Theory course, built by experts for you. December 18, at am. Pattern Finding A problem like this can be tackled by listing out the initial expansions of a power in order to determine a pattern. We can use this fact to decompose the congruence into easier ones:. The set of last digits of powers forms a periodic sequence with periods given by the table below:. Shahil Raza says:. Note: To verify the above result, we can use the concept of binomial expansion. Solving these types of problems gives a down-to-earth introduction to these techniques of elementary number theory. October 12, at am. January 7, at am. Save my name, email, and website in this browser for the next time I comment. Rakesh Vishwakarma 27 Comments. Rudranil Ghosh says:. For example, the last digit of various powers of 1 to 9 are:. April 7, at am.