This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Find the prime factors of 72. Divide 72 by the smallest prime number, 2. 72 ÷ 2 = 36 Divide 36 by 2. 36 ÷ 2 = 18 Divide 18 by 2. 18 ÷ 2 = 9 Now, 9 is not divisible by 2. Divide 9 by the next smallest prime number, 3. 9 ÷ 3 = 3 Divide 3 by 3. 3 ÷ 3 = 1 The prime factors of 72 are 2, 2, 2, 3, 3. Step 2: Write the prime factorization using exponents. Count the occurrences of each prime factor: The prime factor 2 appears 3 times, so it can be written as 2^3. The prime factor 3 appears 2 times, so it can be written as 3^2. Step 3: Combine the exponential forms to get the prime factorization of 72. 72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2 The prime factorization of 72 is 2^3 × 3^2. That's 2 down. 3 left today — send the next one.