Latest cat Aptitude Question SOLUTION: Q. What will be the remainder when (32^32^32) is divided by 7.

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Q. What will be the remainder when (32^32^32) is divided by 7.

Asked In cat Prabhakar Sony (10 years ago)

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arun m d  (10 years ago)

a^b^c is a^(b*c)
hence 32^32^32 is 32^(1024)
32^1024 mod 7 is= (32^2) ........512 times mod 7
by the modulus formula ab mod x can be rewritten as a mod x * b mod x
hence 32^2 mod 7 * 32^2 mod 7 *....................(512 times)
2*2*.....(512 times) mod 7
2^512 can be rewritten as (2^3)^170 * 4 mod 7
2^3 mod 7 is 1 and 1^170 is 1
1*4 is 4
hence answer is 4.

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MD SOHAIL AKHTER  (10 years ago)

rem(32/7)=4
rem(4^2*(4^3)^10^32)/7= rem[(16/7)*rem((64/7)^10^32)= 2*1= 2

the remainder will be 2

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navin   (10 years ago)

ans is 1.
first, we can reduce question to 32^64.
now 32*32*32........ (64 times)/7
dividing single 32 by 7 will give remainder 4.
now we get, 4*4*4.........(64 times)/7
or 16*16*16.............(32 times)/7
after dividing 16 by 7 we get 2 rmainder thus
it becomes, 2*2*2......(32 times)/7
or 8*8*8.........(8 times)/7
after dividing 8 by 7 we get remindr 1.
thus, 1*1*1......(8 times)/7
finally we get, 1/7=1.
remainder is 1.

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navin   (10 years ago)

ans is 4.
32^1024

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rohitashwa  (10 years ago)

32^32^32/7==4^32^32/7 now cyclicity of 7 ==3(4,1,2,again 4) now 32^32 /3==-1^32=1.so 4^1=4 ans

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jitin taneja  (10 years ago)

ans is 4 becauslate after calcu

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