Factorial 2016 in base 7

Number Theory Level pending

Find the number of zeros on the right end of factorial $\color{#3D99F6} {\large (2016_7) ! }$

Note: $\color{#3D99F6} {\large (2016_7) }$ means that the number is in base 7.

The answer is 115.

1 solution

Ossama Ismail
Apr 1, 2016

In base 7, digit zero comes from 7 and its multiples $7 , 7^2, 7^3, .....,etc$ ,

$2016_7 = 699_{10}$

number of zeros = $\lfloor{ \frac {699} {7} } \rfloor + \lfloor{ \frac {699} {7^2} } \rfloor + \lfloor{ \frac {699} {7^3} } \rfloor = 99 + 14 + 2 = 115$

Factorial 2016 in base 7

The answer is 115.

1 solution

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