Question

Coin Collecting The U.S. Mint began issuing state quarters in 1999. There was one state quarter for each of the 50 states. You are collecting the state quarters and want to design a rectangular display with the same number of quarters in each row. How many ways can you arrange your display?

Short answer

We can arrange our display in5 ways. Those are:

There can be 1 row of 50 quarters.

Or, 2 rows of 25 quarters in each row.

Or, 5 rows of 10 quarters in each row.

Or, 10 rows of 5 quarters in each row.

Or, 25 rows of 2 quarters in each row.

Step-by-step solution

Step-1 – Given

Given that there is one state quarter for each of the 50 states. And the rectangular display has same number of quarters in each row.

Step-2 – To determine

We have to find the number of ways in which display can be arranged.

Step-3 – Calculation

We can write 50 as a product of two of its factors as given below:

$\begin{array}{c}50=1\times 50\\ 50=2\times 25\\ 50=5\times 10\end{array}$

This means that we can arrange them as:

1 row of 50 quarters.

Or, 2 rows of 25 quarters in each row.

Or, 5 rows of 10 quarters in each row.

Or, 10 rows of 5 quarters in each row.