Latest Others Aptitude Question SOLUTION: what are the last two digits of 3^1997

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what are the last two digits of 3^1997

Asked In Others Harsh Poddar (10 years ago)

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akanksha   (10 years ago)

Considering only last two digits:
3^0= 01
3^1= 03
3^2= 09
3^3= 27
3^4= 81
3^5= 43
3^6= 29
3^7= 87
3^8= 61
3^9= 83
3^10= 49
3^11= 47
3^12= 41
3^13= 23
3^14= 64
3^15= 07
3^16= 21
3^17= 63
3^18= 89
3^19= 67
3^20= 01 (same as 3^0=01)

As we can see, Pattern repeats itself every 20th exponent.

Now 1997/20= 99.85

Take only integer part and multiply by 20 = 99*20 = 1980

Subtract it from 1997 => 1997-1980 = 17

Hence, the last two digits will be the same as that of 3^17=63

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