First factor the numerator and denominator.

8n =  2 · 2 · 2 · n

16n =  2 ·  2 · 2 · 2 · n

The GCF is the product of the common prime factors in each term.

GCF = 2 · 2 · 2 · n = 8n \ \

The GCF of 8n, 16n is 8n.