G1.1 Given that $a$ is an integer. If 50 ! is divisible by $2^{a}$, find the largest possible value of $a$.
$2,4,6,8, \ldots, 50$ are divisible by 2 , there are 25 even integers.
Reference: 1990 HG6, 1994 FG7.1, 1996 HI3, 2004 FG1.1, 2011 HG7, 2012 FI1.4, 2012 FG1.3
$4,8, \ldots, 48$ are divisible by 4 , there are 12 multiples of 4 .
$8, \ldots, 48$ are divisible by 8 , there are 6 multiples of 8 .
$16, \ldots, 48$ are divisible by 16 , there are 3 multiples of 16 .
32 is the only multiple of 32 .
$$
a=25+12+6+3+1=47
$$