Analyze Option A

Factors of $455 = 5 \times 7 \times 13$. Factors of $49 = 7 \times 7$. Since they share the common factor $7$, they are not co-prime.

$\text{gcd}(455, 49) = 7 \neq 1$

Analyze Option B

Factors of $81 = 3^4$ ($3, 9, 27, 81$). Factors of $16 = 2^4$ ($2, 4, 8, 16$). They share no common factors other than 1.

$\text{gcd}(81, 16) = 1$

Analyze Option C

Factors of $363 = 3 \times 11^2$. Factors of $77 = 7 \times 11$. Since they share the common factor $11$, they are not co-prime.

$\text{gcd}(363, 77) = 11 \neq 1$

Analyze Option D

Factors of $52 = 2^2 \times 13$. Factors of $24 = 2^3 \times 3$. Since they share the common factor $2$, they are not co-prime.

$\text{gcd}(52, 24) = 4 \neq 1$