A) 9
B) 5
C) 18
D) 10
Correct Answer: C
Solution :
We know that, if\[a=p_{1}^{{{\alpha }_{1}}}\cdot p_{2}^{{{\alpha }_{2}}}\] 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, \[{{\alpha }_{1}}=2,\,\,{{\alpha }_{2}}=2,\,\,{{\alpha }_{3}}=1\] \[\therefore \] \[T(a)=(2+1)(2+1)(2+1)\] \[=3\cdot 3\cdot 2\] \[=18\]
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