For any number \(N\) which can be written in it's factor form as \((a^x)(b^y)(c^z)....\), Total number of factors is given by \((x+1)(y+1)(z+1)....\)

Let, \(N = a^x\)
So, total factors \(= (x+1) = 7\)
i.e. \(x = 6\)

\(N = a^6\)
Since, N is the smallest number \(a = 2\)
Therefore, \(N = 2^6 = 64\)

Col. A: Factors of \(\sqrt{64}\)
Col. B: Factors of \((64-2) = 62\)

Col. A: \(\sqrt{64} = 8 = 2^3\)
Col. B: 62 = (2)(31)

Using the same formula above;

Col. A: Factors of \(8 = (3+1) = 4\)
Col. B: Factors of \(62 = (1=1)(1+1) = 4\)

Hence, option C