Let us start this article with a question
Question:
What is the unit digit of\(1234^{567}\) ?
Question:
What is the unit digit of\(1234^{567}\) ?
- To be able to answer the above question, we need to understand what ‘cyclicity’ is and how it is related to unitdigits
- Let us take the example of 2 and its multiple positive integral power like\( 2^1, 2^2,2^3\) and so on
Attachment:
cyclicity1.png
- If you look closely, you will notice a pattern of 2, 4, 8, and 6 and the pattern repeats itself after every 4thpower
- Unit digit of\(2^5\) is the same as the unit digit of\(2^1\)
- Unit digit of\(2^6\) is the same as the unit digit of\(2^2\)
- Unit digit of\(2^7\) is the same as the unit digit of\(2^3\)
- Unit digit of\(2^8\) is the same as the unit digit of\(2^4\)
- This pattern continues throughout
- Does this mean that every number will show the same pattern as 2? 🤔
- Well, let us check one more number. Say for4
Attachment:
cyclicity2.png
- We see that in the case of 4, the repeating numbers are[color=#8dc73f] 4 and 6 and this pattern repeats
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Attachments
cyclicity4.png [ 20.72 KiB | Viewed 42 times ]
cyclicity3.png [ 26.26 KiB | Viewed 42 times ]
cyclicity2.png [ 22.68 KiB | Viewed 42 times ]
cyclicity1.png [ 34.35 KiB | Viewed 42 times ]
Statistics : Posted by SaquibHGMATWhiz • on 21 Nov 2022, 08:15 • Replies 0 • Views 43
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