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Question

N=7!3. How many factors of N are multiples of 10?

A
736
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B
1008
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C
1356
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D
894
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Solution

The correct option is B 1008
Prime factorization of (7!)3=(24×32×5×7)3=212×36×53×73
Now, for a multiple of 10, there should be at least one 5 and at least one 2 present in the number.
Therefore, the number can be like =2112×306×513×703
Hence, number of factors =12×7×3×4=1008

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