Target Test Prep Sample Total Digits Question

Solution:

The first step is to prime factorize the number  ${50}^8\times 8^3\times {11}^2$. This becomes:

$\begin{array}{l}\Rightarrow {50}^8\times 8^3\times {11}^2\\ \Rightarrow {\left(5\times 5\times 2\right)}^8\times \left(2^9\right)\times {11}^2\\ \Rightarrow 5^{16}\times 2^8\times 2^9\times {11}^2\\ \Rightarrow 5^{16}\times 2^{17}\times {11}^2\end{array}$

The sixteen (5 × 2) pairs contribute a total of sixteen trailing zeros to the number. One 2 and two 11's remain. The product of (2 × 11 × 11) = 242, which is 3 digits. Thus, the number has (16 + 3) = 19 total digits.