Latest Others Aptitude Question SOLUTION: what is the remainder when 7^105 is divided by 25

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what is the remainder when 7^105 is divided by 25

Asked In Others Harsh Poddar (10 years ago)

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Saraswathy  (10 years ago)

7^1 % 25 = 7
7^2 % 25 = 24
7^3 % 25 = 18
7^4 % 25 = 1
7^5 % 25 = 7
7^6 % 25 = 24
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So it continues like 7, 24, 18, 1, 7, 24... (4 cycles)

105/4= 26 * 4 + 1 [Since v have 4 cycles, v divide it by 4]

it completes 26 cycles of {7, 24, 18 ,1} and again continues from 7

So the remainder is 7

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akanksha   (10 years ago)

7^0/25= 0 with remainder 1
7^1/25= 0 with remainder 7
7^2/25= 1 with remainder 25
7^3/25= 13 with remainder 18
7^4/25= 96 with remainder 1(repeating pattern)

Hence every 4th exponent, pattern is repeating.
105/4 = 26.25
Take only integer part and multiply by 4=> 26*4= 104
Subtract it from 105 to get 1

Hence, answer is same remainder as that of 7^1 ie 7

(MAYBE)

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