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the largest non - negative integer K ...

the largest non - negative integer K such that `24^(k) ` divides 13! Is -

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
when m is maximum possible value
& n is also maximum possible value
so m `=[(13)/(2)]+[(13)/(4)]+[(13)/(8)]+[(13)/(16)]+* * *`
`=6+3+1`
` =10`
`n=[(13)/(3)]+[(13)/(9)]+[(13)/(37)]+.*.*`
`=2+1`
`=3`
`So , 13!=2^(10).3^(3) lamda.`
`2.(2^(3).3)(2^(3) .3)(2^(3) .3)lamda.`
` =2(24)^(3) lamda.`
`:' k=3`
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