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find the remainder when 3^164 divided by 162
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- remainder is 1...
we can write 162 as 2*81=2*(3^4)
so (3^164)/(2*(3^4))=(3^160)/2
3 power any thing will result an odd integer... ( like 3,9,27,81...)
so 3^160 is an odd integer...
we all know any odd integer divided by 2 will result 1 as remainder...
so 1 is the remainder... - 12 years agoHelpfull: Yes(18) No(4)
- 3^1=3
3^2=9
3^3=27 units place 7
3^4=81 units place 1
---------------------
3^5=243 units place 3
3^6=--9 units place 9
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3^160=----1 units place 1
3^164/162=3^164/2*3^4
=3^160/2
=(---1)/2=rem(1)
so, remainder=1 - 12 years agoHelpfull: Yes(3) No(4)
- For x ≥ 4, Remainder (
3x
81
)=0
And, Remainder (
3x
162
)= 81 - 10 years agoHelpfull: Yes(1) No(1)
- ans is 81
- 8 years agoHelpfull: Yes(1) No(0)
- Answer is 2.
1+6+4=11. Nearest multiple of 3 is 9. So the difference is remainder = 2. - 12 years agoHelpfull: Yes(0) No(16)
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