6 50 215 Find Remainder

6^50/215
= (6^3)^16*6^2/215
= (216)^16 * 6^2 /215
= (215 + 1)^16 * 6^2 /215
By remainder theoram,
215+1/215 = 1
hence, ans : 6^2/215 = 36 remainder
10 years agoHelpfull: Yes(7) No(0)
since,6^0/216=1/216=1
6^1/216=6/216=6
6^2/216=36/216=36
6^3/216=216/216=1
6^4/216=1296/216=6
since it is repeating after 3 times,so
((6^48)*(6^2))/216
6^48/216=1 & 6^2/216=36
answer is 36
10 years agoHelpfull: Yes(5) No(0)
36 may be the answer.
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Divya can u explain me how it is 36
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36,(216)/215 rem-1
((6^3)^48)*6*6)=1^48*6*6=36
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(((6^3)^16) * 6 *6))/215
216*36/215
(215+1)/36
rem 36
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remainder is 36
(6^3*15)*(6^5)/215
(1)^15*6^5/215
6^5/215
36/215
rem:36
9 years agoHelpfull: Yes(1) No(0)
36
(6^(3*16).6^2)/(6^3-1)
when (6^(3*16) is divided by (6^3-1) remainder will be 1 so 1*36=36
10 years agoHelpfull: Yes(0) No(0)
@Durga (6^50) can be written as ((6^3)^16.6^2)=> (216^16*6^2)/215
=> (1^16 * 36)/215 (since 216/215 gives 1 as the remainder)
=> (1*36)/216
finally the remainder is 36
10 years agoHelpfull: Yes(0) No(0)
6^50=(6^48)*(6^2)=((6^3)^16)*6^2=(216^16)*36.
so,((216^16)*36))/215 ---> (R(216/215))^16 * (R(36/215)).
216-215=1. AND HENCE 1*36=36. I MEAN 36/215 is the resultwe are gettng.so remainder is 36.
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The remainder is 16
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answer is 37
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6^50 / 215
Find Remainder..