How was Constantinople in 1453 a factor in the age of exploration?

To actually answer your question the fall of Constantinople was a major factor as it allowed the Ottoman Empire to strengthened its control over trade with the East as at the time only over land trade routes with China and India (the two richest countries at the time) existed. Western European States were faced with higher tariffs and disruptions when war broke out between the Ottomans and their neighbours. Portugal was the first to make a breakthrough when they successfully chartered a trade route to what is now Goa in India by sailing around the Cape of Good Hope at the southern tip of Africa. This trade route was kept secret and so other countries were still faced with the difficulties of the over land trade routes. It is for this reason that Isabella of Spain agreed to patronise Columbus' attempt to find an alternative.