1. **Problem Statement:** Find the Least Common Multiple (L.C.M) and Greatest Common Factor (G.C.F) of 32 and 58. 2. **Definitions:** - The G.C.F (also called GCD) of two numbers is the largest number that divides both without leaving a remainder. - The L.C.M of two numbers is the smallest number that is a multiple of both. 3. **Step 1: Prime Factorization** - 32 = $2^5$ - 58 = $2^1 \times 29$ 4. **Step 2: Find G.C.F** - Take the lowest powers of common prime factors. - Common prime factor is 2. - Lowest power of 2 is $2^1 = 2$. - So, G.C.F = 2. 5. **Step 3: Find L.C.M** - Take the highest powers of all prime factors present. - For 2: highest power is $2^5$. - For 29: highest power is $29^1$. - So, L.C.M = $2^5 \times 29 = 32 \times 29 = 928$. 6. **Final Answer:** - G.C.F of 32 and 58 is 2. - L.C.M of 32 and 58 is 928.