17 votes 17 votes What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$ Quantitative Aptitude tifr2018 quantitative-aptitude modular-arithmetic + – Arjun asked Dec 10, 2017 recategorized Nov 21, 2022 by Lakshman Bhaiya Arjun 3.2k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes (4444)4444 % 9 = (4444 % 9)4444 % 9 = 77 % 9 = (72.72.72.7) % 9 = (343.343.343.7) % 9 = 1.1.1.7 = 7 OPTION (D) rfzahid answered Dec 10, 2017 rfzahid comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $4444^{4444}\;mod\;9$ $=(4437+7)^{4444}\;mod\;9 $ (4437 is the nearest number(<4444) which is divisible by 9) $=7^{4444}\;mod\;9$ $=(7^3)^{1481}\times 7\;mod\;9$ $=7\;mod\;9$ $=7$ Verma Ashish answered Aug 21, 2019 Verma Ashish comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Answer : D apply fermat's little theorem , 4444 , 9 are relatively prime , so you can apply make sure power of 4444 should be multiple of 8, floor(4444/8) = 555 so , ((4444)^(555*8)) *(4444)^4 mod9 = 1*4444^4 mod9 4444 mod 9 = 7. so, 7^4 mod9 = 7 shivam001 answered Jan 29, 2020 shivam001 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes $4444^{4444}\ mod\ 9$ = $4444^{(3*1481)+1}\ mod\ 9$ = $(4444^{(3*1481)} * 4444 ^1)\ mod\ 9$ =$(4444^{(3*1481)}\ mod\ 9 )* (4444\ mod\ 9) $ =$(4444^{3}\ mod\ 9 )^{1481}* (4444\ mod\ 9) $ =$(87765160384\ mod\ 9 )^{1481}* (4444\ mod\ 9) $ =$1^{1481}*7$ =$7$ Satbir answered Jun 25, 2019 Satbir comment Share Follow See all 0 reply Please log in or register to add a comment.