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 120. Divide 120 by the smallest prime number, 2. 120 ÷ 2 = 60 Divide 60 by 2. 60 ÷ 2 = 30 Divide 30 by 2. 30 ÷ 2 = 15 Now, 15 is not divisible by 2. Divide 15 by the next smallest prime number, 3. 15 ÷ 3 = 5 Now, 5 is not divisible by 3. Divide 5 by the next smallest prime number, 5. 5 ÷ 5 = 1 The prime factors of 120 are 2, 2, 2, 3, 5. 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 1 time, so it can be written as 3^1 or simply 3. The prime factor 5 appears 1 time, so it can be written as 5^1 or simply 5. Step 3: Combine the exponential forms to get the prime factorization of 120. 120 = 2 × 2 × 2 × 3 × 5 = 2^3 × 3 × 5 The prime factorization of 120 is 2^3 × 3 × 5. Last free one today — make it count tomorrow, or type /upgrade for unlimited.