Sam Loyd's Battle of Hastings Puzzle - Solution

The Puzzle:

Sam Loyd's Battle of Hastings Puzzle
In the Battle of Hastings that occurred on October 14, 1066 Harold's forces formed 13 similar squares with exactly same number of soldiers in each square.

When Harold himself joined the fray and was added to the number of his soldiers in those thirteen squares a single huge square could be arranged. How many men there must have been in Harold's force?

Our Solution:

Harold had thirteen squares of 180 men on each side, which would give 180x180x13=421,200 men.

This number, with Harold added, would form one great square with 649 men on the sides.
Puzzle Author: Loyd, Sam

See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum