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  • The sum of the factors of 9 ! which are odd and are of the form , where <img alt="\

The sum of the factors of 9 ! which are odd and are of the form \mathrm{3 m+2}, where \mathrm{m} is a natural number is

Option: 1

40


Option: 2

45


Option: 3

51


Option: 4

54


Answers (1)

best_answer

We have 9 !=2^{7} \times 3^{4} \times 5 \times 7

Odd factors of the form \mathrm{3 m+2} are neither multiples of 2 nor multiples of 3 . So the factors may be \mathrm{1,5,7,35}  of which just 5 and 35 are of the form \mathrm{3 m+2}. Their sum is 40.

Posted by

Gautam harsolia

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