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I have posted a video on YouTube to discuss Units' Digit of Power of 8
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
Theory of Units' Digit of Power of 8
⁍ Find Units’ digit of \(8^{91}\) ? ⁍ Find Units’ digit of \(8^{57}\) ? ⁍ Find Units’ digit of \(8^{88}\) ? ⁍ Find Units’ digit of \(8^{40a + 41}\) (given that a is a positive integer)? ⁍ Find Units’ digit of \(1757^{8979}\) ?
Theory of Units' Digit of Power of 8
• To find units' digit of any positive integer power of 8
We need to find the cycle of units' digit of power of 8
\(8^1\) units’ digit is 8 \(8^2\) units’ digit is 4 \(8^3\) units’ digit is 2 \(8^4\) units’ digit is 6
\(8^5\) units’ digit is 8 \(8^6\) units’ digit is 4 \(8^7\) units’ digit is 2 \(8^8\) units’ digit is 6
=> The power repeats after every \(4^{th}\) power => Cycle of units' digit of power of 8 = 4 => We need to divide the power by 4 and check the remainder => Units' digit will be same as Units' digit of \(8^{Remainder}\)
NOTE: If Remainder is 0 then units' digit = units' digit of \(8^{Cycle}\) = units' digit of \(8^{4}\) = 1
Sol: We need to divided the power (81) by 4 and get the remainder 81 divided by 4 gives 1 remainder => Units' digit of \(8^{81}\) = Units' digit of \(8^1\) = 8
Sol: Units' digit of power of any number = Units' digit of power of the units' digit of that number => Units’ digit of \(1758^{8979}\) = Units’ digit of \(8^{8979}\) => Remainder of 8979 divided by 4 = Remainder of last two digits by 4
How to Solve: Units' Digit of Power of 8
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26 Aug 2024, 20:30
1
Thank you for reading the post and sharing the comment.
dipenshome wrote:
For Q3, I think the answer provided is wrong. If Remainder is 0 then units' digit will be 6, not 1. Unit Digit of \(8^4 = 6\)
You are correct, there was a typo. Unit's digit of \(8^4\) = 6 as mentioned in the pattern in the post above. Post has been corrected to reflect the same. Thank you.
dipenshome wrote:
The answer for Q5 doesn't make any sense.
Yes, the question is 1758^8979 Post has been corrected to reflect the same. Thank you.
gmatclubot
How to Solve: Units' Digit of Power of 8 [#permalink]