Explanation:

The term 14! equals the product of the numbers 1,2,3,4,5,6,7,8,9,10,11,12,13 and 14.

Only two of these numbers are divisible by 7.

The numbers are 7 and 14.

Hence, 14! can be expressed as the product of k×7×14, where k is not divisible by 7.

k×7×14 contains two 7's in it.

Hence, the maximum value of m is 2.