1. **Problem 36:** Determine which of the given numbers divides $2^{15}$. 2. Recall that $2^{15} = 32768$ and is a power of 2, so its prime factorization is only 2's. 3. For a number $x$ to divide $2^{15}$, $x$ must be a power of 2 or a product of powers of 2 only. 4. Check each option: - A) 20 = $2^2 \times 5$ (contains prime factor 5, so cannot divide $2^{15}$) - B) 30 = $2 \times 3 \times 5$ (contains prime factors 3 and 5, so cannot divide $2^{15}$) - C) 12 = $2^2 \times 3$ (contains prime factor 3, so cannot divide $2^{15}$) - D) 32 = $2^5$ (only prime factor 2, and $5 \leq 15$, so divides $2^{15}$) 5. **Answer for problem 36:** D) 32 1. **Problem 37:** Identify which of the given numbers is prime. 2. Recall prime numbers are numbers greater than 1 with no divisors other than 1 and itself. 3. Check each option: - A) 44 is even and divisible by 2, so not prime. - B) 53 is a known prime number. - C) 27 = $3^3$, so not prime. - D) 81 = $3^4$, so not prime. 4. **Answer for problem 37:** B) 53