How to Find Last Digits of Large Powers and Exponents | GMAT Shots | Experts' Global GMAT Prep

Learn how to find the last digit of units digit of expressions such as 3^100 or 2^51 in less than a minute! Helpful for GMAT quantitative section.
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[@ExpertsGlobal-GMAT-Admissions]

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[@EliGoncharov]

For anyone coming here from CodeWars (Last digit of a large number), this is it

[@justjhonmichael7815]

bloody kata hahah

[@brahimoukhouya5888]

The thing is I always like to make a mathematical proof. But fearing that I might have went into the wrong way I tried to check. I mean the algorithm is neat. but what is better is to have a full fledged proof

[@hydox7098]

why do you choose remainder 4 if the remainder is 0?

[@abdusoliergashev7286]

It is really cool, easy method

[@RyanLewis-Johnson-wq6xs]

537^3958 ends in 9

[@adhyuthnarayan]

Awesome method

[@ashishsinha9035]

Thanks!

[@LiMinhh_Heng]

Could you detail more about the remainder

[@null7953]

What if the base is 1? For example 11^8012. The base is always 1. So the last digit is always 1?

[@mayanksrivastava5246]

That’s correct. When base is 0, 1, 5, or 6, the latest digit remains the same- 0, 1, 5, 6 respectively.

[@null7953]

What if I wanted to get the last 4 digits of the number what do I need to do

[@mayanksrivastava5246]

Even through a shortcut, that would be bulky and thus, beyond the scope of any aptitude test where a question must be solvable in 2 mins :)

[@null7953]

I need to do it for an assignment :(

[@indiankidtuber3247]

@@mayanksrivastava5246 What if I'm asked to get the last to digits? Is there any way to do that??

[@mrvenky5292]

Tqsm

[@fantasy7432]

Thank you

[@rabekasultana7097]

thank you alot!! helps a lost!!

[@entertainer05060]

Wow method😊

[@syedusamamanzoor1838]

love you...............

[@roberttrooper]

I am looking for a method to find the last two digits of 6^128. Thank you.

[@ExpertsGlobal-GMAT-Admissions]

Write it as 36^64. Now, look for pattern in the last two digits of higher powers of 36. You will find that the pattern is (36, 96, 56, 16, 76, 36...). Hence, the cyclicity is 6. 64% 6 = 4. Hence, the answer is going to be the "4th" term in the series- 36, 96, 56, 16, 76, 36. The answer is "16". Hope this helps. Experts' Global expertsglobal.com

[@anaghamohan3731]

❤❤

[@thamidurandilbandara415]

well this does not work for all the numbers does it?

[@ExpertsGlobal-GMAT-Admissions]

It does. Please watch the video carefully 🙏

[@kristijanbogoev5238]

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[@harshavardhanvatti8501]

Tq air

[@harshavardhanvatti8501]

Sir not air

[@lamha8801]

Why is divided by 4?

[@ExpertsGlobal-GMAT-Admissions]

Some digits (2,3,7,8) repeat after cycles of 4 Some digits (4,9) repeat after cycles of 2 Some digits (1,3,5,6) repeat everytime and thus, repeat in cycles of '1'. As '1' and '2' are factors of '4', all digits repeat after cycles of '4'. Hence, '4' works for all digits. Thanks Experts' Global expertsglobal.com

[@noemibedic3945]

proof?

[@ojasvivaish3203]

Kewlll

[@bootyslayer4]

17^13, last digit is 6 13/4 = 3, remainder is 1 7^1 = 7 7 =/= 6

[@ExpertsGlobal-GMAT-Admissions]

Hello, I am not sure how you suddenly got 6 in the final step. Please watch the video carefully. The last digit of 17^13 is definitely 7. Think, Odd raise to power any integer will always be an odd number so the last digit cannot be 6. Please watch the video carefully. On a humble note, the correct way to learn is that when you disagree with something, ask yourself "What am I missing" rather than assuming a source to be incorrect. All the best! Experts' Global www.ExpertsGlobal.com