Step 1: Understand the process of tree aging.
The age of a tree is typically determined by studying its growth patterns, which are recorded within its trunk.
Step 2: Identify the primary method for age determination.
The most reliable and common method to ascertain the age of a tree is by counting its annual rings (also known as growth rings or tree rings). Each ring generally represents one year of growth, with a wider ring indicating a good growing season and a narrower ring indicating a poorer one. This field of study is called dendrochronology.
Step 3: Evaluate the given options.
Option 1: Radius of its stem. While the radius is related to the tree's growth, it doesn't directly indicate age without knowing the growth rate, which can vary significantly.
Option 2: Circumference of its stem. Similar to the radius, circumference is a measure of size, not a direct indicator of age. Two trees of the same circumference can have very different ages depending on their species and growing conditions.
Option 3: Number of branches. The number of branches is not a consistent indicator of a tree's age. Branching patterns can be influenced by many factors, including species, environment, and pruning.
Option 4: Number of annual rings. This is the accurate method. Each annual ring represents one year of the tree's life, and counting them provides a direct measure of its age.
The final answer is $\boxed{\text{4}}$.