A) \[9\]
B) \[5\]
C) \[18\]
D) \[10\]
Correct Answer: C
Solution :
We know that, if \[a=p_{1}^{{{\alpha }_{1}}}.p_{2}^{{{\alpha }_{2}}}....\] Then, the total number of positive divisors of a is \[T(a)=({{\alpha }_{1}}+1)\,({{\alpha }_{2}}+1).....\] Given, \[252={{2}^{2}}\times {{3}^{2}}\times {{7}^{1}}\] Here, \[{{\alpha }_{1}}=2,\,{{\alpha }_{2}}=2,{{\alpha }_{3}}=1\] \[\therefore \] \[T(a)=(2+1)\,(2+1)(1+1)\] \[=3.3.2\] \[=18\]
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