Latest Technical Aptitude Question SOLUTION: What is the unit digit of 7777^3333-3333^7777, give the answer with the explanation

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What is the unit digit of 7777^3333-3333^7777, give the answer with the explanation

Asked In Technical Vaibhav Lokesh (9 years ago)

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Rubina   (9 years ago)

7^3333=(7^4)^833*7=7
As cyclicity of 7is 4 so 7^4=1
3^7777=(3^4)^1944*4=4
As cyclicity of 3 is 4 so3^4=1
7-4=3 is the and.

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ajay kulkarni  (9 years ago)

Ans is 4
7777^1...unit digit is 7 as 7^1
7777^2...unit digit is 9 as 7^2
7777^3...unit digit is 3 as 7^3
7777^4...unit digit is 1 as 7^4
7777^5...unit digit is 7 as 7^5. Hence after every forth power unit digit cycle is repeated.
(7777^3332)*(7)=(unit digit is 1)*7=7
3333^1.....unit digit is 3 as 3^1
3333^2.....unit digit is 9 as 3^2
3333^3.....unit digit is 7 as 3^3
3333^4.....unit digit is 1 as 3^4
3333^5.....unit digit is 3 as 3^5. Hence after every forth power unit digit cycle is repeated.
(3333^7776)*3=(unit digit is 1)*3=3
Hence 7-3=4

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