Latest TCS Aptitude Question SOLUTION: what is the remainder when 128^1000 is divided by 153.

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(#M40030223) TCS Numerical Ability question REMAINDER Keep an EYE

what is the remainder when 128^1000 is divided by 153.

Asked In TCS Kuldeep (10 years ago)

Solved RAKESH Read Solution (13)

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RAKESH  (10 years ago)

128^1000/153
=(16384)^500/153
=(153*107+13)^500/153
=13^500/153
=169^250/153
=(153+16)^250/153
=16^250/153
=(4096^83)*16/153
=(153*27-35)^83*16/153
=(-35)^83*16/153
=(1225)^41*16*(-35)/153
=(153*8+1)^41*16*(-35+153)/153
=16*118/153=1888/153 gives remainder 52
ans 52

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RAKESH  (10 years ago)

128^1000/153
=128^1000/9*17
now 128^1000/9=2^7000/9=(2^3)^2333*2/9=(9-1)^2333*2/9=(-1)^2333*2/9=-2/9 gives ramainder 7 so canbe written as 9x+7
and 128^1000/17=(2^4)^1750/17=(17-1)^1750/17 gives remainder 1 so canbe written as 17y+1
solve 9x+7=17y+1, for least +ve integral value of x or y
or 9(x-y)=8y-6
or y=3,x=5
hence remainder is 9x+7=9*5+7=52
0r 17y+1=17*3+1=52
ANS 52

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vinit agarwal  (10 years ago)

ans: 52
128^2/153 gives remainder 13
13^2 gives remainder 16
16^2 gives remainder 103
103^2 gives 52
so going on
103^2/153
remainder 52

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Parun  (10 years ago)

Remainder will be 52
It can be solved by remainder theorem

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Manuj Vishnoi  (10 years ago)

explain it

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Mahesh  (10 years ago)

I have done this in a slightly crude method.I will try to find a more refined method.

(2^7)^1000 is 2^7000 = (2^5)^1400

When powers of 32 are divided by 155, it will follow a cycle of 32, 94, 63 and 1.
The cyclicity is 4.

S0,(32)^1400 is ((32)^4)^350 so the remainder is (1)^350

The remainder is 1

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rajat kumar  (10 years ago)

bhaiyo aur deviyo ans. is 52..........
bhavnao me beh gya tha..

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Shivangi Nagar  (10 years ago)

128^2%153 gives remainder 13
13^2%153 gives remainder 16
16^2%153 gives remainder 103
103^2%153 gives remainder 52
52^2%153 gives remainder 103(here cycle repeats)
so remainder is 52...
128^2%153 gives remainder 13
128^2%153 gives remainder 13

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Nitika Sharma  (10 years ago)

what`s the right answer?

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juhe rawat  (10 years ago)

what is remainder theorm

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rajat kumar  (10 years ago)

Ans. is 103
rok ske to rok lo

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Amlan Mohanty  (10 years ago)

i think d answer is 16.

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p saha  (1 year ago)

Answer will be 128

because,
rem = 128-153 = -25
but rem can not be -ve so
rem = [ 153 - 25 ] = 128( final ans)

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