Linked from
The 11 pages that link to Stirling's approximation, each with the reason it gives.
FactorialRelated: It estimates factorials too large to compute directly.
Gamma functionRelated: It describes how Γ(z) grows when its argument becomes large.
PiRelated: Its leading expression includes √(2πn), linking pi to factorial growth.
Root testRelated: It evaluates root-test limits for terms containing factorials.