123 ! Is exactly divisible by `(251) ^(x)` Find the max. value of x.

123! Is exactly divisible by (25!)^(x) Find the max value of x.

If 133! Is exactly divisible by 6^(n) . Find the max. value of n.

If 133 ! Is exactly divisible by 6^(n) find the max value of n.

123 ! Is exactly divisible by 12 ^(n) . Find max. value of n.

If 187 ! is exactly divisible by 15^(n) . Find max. value of n.

If x^(3) +ax^(2) + 2x+3 is exactly divisible by (x+1) . Find the value of a

If the polynomial x^(4)-3x^(3)-6x^(2)+kx-16 is exactly divisible by x^(2)-3x+2 , then find the value of k .

If x+ y= 6 then max value of xy

If the polynomial 4x^(3)-16x^(2)+ax+7 is exactly divisible by x-1, then find the value of a. Hence factorise the polynomial.