Step 1

Consider the given number 7875.

Step 2

Obtain the prime factorization of the number 7875 as follows.

\(7875 = 3\times 2625\ \ \ [3\times 2625 = 7875]\)

\(=3\times 3\times 875\ \ \ [3\times 875 = 2625]\)

\(=3\times 3\times 5\times 175\ \ \ [5\times 175=875]\)

\(=3\times 3\times 5\times 5\times 35\ \ \ [5\times 35=175]\)

\(=3\times 3\times 5\times 5\times 5\times 7\ \ \ [5\times 7 = 35]\)

\(=3^{2}\times5^{3}\times7\)

Thus, the prime factorization of the number 7875 is \(3^{2}\times5^{3}\times7\).