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CBSE Class 11-science Answered

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Asked by Kchawla94 | 25 Mar, 2019, 09:27: PM
answered-by-expert Expert Answer
In 1337, unit digit is 7.
 
when 7 is multiplied by itself several times, we get a periodic sequence of unit digit for every 4 times as explained below
 
7,    72 =49 ,  73 = 343,   74 = 2401   : unit digits are  7, 9, 3 and 1  and this repeats after every 4 multiplications.
 
Similarly for the number 13,  unit digit 3 follow the sequence when it is multiplied by itself for every 4 multiplications as shown below
 
3,  32 = 9,  33 = 27,  34 = 81, the sequence of unit digits 3,9,7 and 1 repeats after every 4 multiplications.
 
similarly unit digit 9 follow the sequence when it is multiplied by itself for every 2 multiplications :  9 , 92 = 81.........etc
 
Hence in the product, (1337)124 (13)9 95
 
7 is multiplied 124 times, at the end of 41th period, unit digit becomes 1
3 is multiplied 9 times, after 2 periods, 9th multiplication gives unit digit as 3
9 is multipied 5 times, after 2 periods, 5th multiplication gives unit digit as 9
 
now the product of all these digits gives 9×3×1 = 27  
 
hence finally we get the unit digit as 7
Answered by Thiyagarajan K | 26 Mar, 2019, 07:46: AM

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