Latest CAT Aptitude Question SOLUTION: highest power on 990 which exactly divide 1090!

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highest power on 990 which exactly divide 1090!

Asked In CAT Supriya (10 years ago)

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Ashutosh Anshu  (10 years ago)

990 = 2*3^2*5*11
now 1090/2+1090/4+1090/8+1090/16+1090/32+1090/64+1090/128+1090/256+1090/512+1090/1024 = 545+272+136+68+34+17+8+4+2+1=1087

1090/3+1090/9+1090/27+1090/81+1090/243+1090/729 = 363+121+40+13+4+1 = 542

1090/5+1090/25+1090/125+1090/625 = 218+43+8+1 = 270

1090/11+1090/121 = 99+9 = 108

therefore min(1087,542,270,108) = 108 answer

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Meghal Aggarwal  (10 years ago)

factors of 990 = 2*3^2*5*11
so the highest power on 990 which exactly divides 1090! is
= [1090/11] + [1090/11^2]
= 99 + 9
= 108

so the highest power is 108

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Vinay Sipani   (10 years ago)

108

990 = 11*10*9

1090! = 1090 * 1089!
1089! has 11,22,33,... , 121,242,363, ... 1089
In total, there are 99 + 9 = 108 => 11^108

=> Highest power of 990 which divides 10901 = 108

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