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Q.
Which of the following is a prime number?
Permutations and Combinations
Solution:
The number $1003, 73271$ and $667$ are respectively divisible by $17, 11$ and $29$ and the number $370261$ have no factor.
(i) $1003 = 17 \times 59 $
(ii) $667 = 23 \times 29$
(iii) $73271= (7 + 2 + 1) - (3 + 7) - 10 - 10 = 0$
As difference of the sum of the number exist at odd and even places is divisible by $11$.