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Home prices and the number of residential sales continue to rise in the Richmond area, according to a report released Monday by the Central Virginia Regional Multiple Listing Service.

However, higher prices here and across the state are being fueled in part by low inventories of houses for sale, according to this report and a separate one also released Monday by Virginia Realtors, a statewide trade group.

In all, 4,462 houses were sold in the third quarter in the Richmond area, up 4 percent from the same period a year ago, according to the local MLS report.

Meantime, the region’s core counties — Chesterfield, Hanover and Henrico — and the city of Richmond posted higher prices.

The median price in the Richmond area, with half the houses selling for more and half for less, was $251,224 in the third quarter, up 7 percent from the same period a year ago. Hanover posted the highest median price of $285,000, up 9 percent from the same period a year ago.

Chesterfield — with 1,801 houses sold in the quarter — had the most sales in the region, up 5 percent from the same period a year ago, followed by Henrico County — 1,400 sales in the quarter — up 4 percent from a year ago.