A) 6, 718, 464
B) 60,418, 464
C) 70, 416, 246
D) 7, 842, 321
Correct Answer: A
Solution :
\[{{(7\times 3)}^{3}}\times {{(17\times 2)}^{2}}\times {{(23\times 2)}^{8}}\times {{(11\times 7)}^{8}}\] \[\Rightarrow \,\,{{(7)}^{3}}\times {{(3)}^{3}}\times {{(17)}^{7}}\times {{(2)}^{7}}\times {{(23)}^{8}}\times {{(2)}^{8}}\times {{(11)}^{8}}\times {{(7)}^{8}}\] Number of factors \[=(3+1)\times (3+1)\times (7+1)\,(7+1)\times (8+1)\times (8+1)\] \[\times (8+1)\times (8+1)\] \[=4\times 4\times 8\times 8\times 9\times 9\times 9\times 9\] \[=6,\,\,718,\,\,464\]
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