Find the prime factorization of 120.

Answer

To find the prime factorization of 120, we will break it down into its prime factors step by step.

**Step 1: Start with the number 120.**
We will begin by dividing 120 by the smallest prime number, which is 2.

**Calculation:**
120 ÷ 2 = 60

**Step 2: Continue factoring 60.**
Now we take the quotient 60 and divide it by 2 again.

**Calculation:**
60 ÷ 2 = 30

**Step 3: Factor 30.**
Next, we take 30 and divide it by 2 once more.

**Calculation:**
30 ÷ 2 = 15

**Step 4: Factor 15.**
Now, we take 15, which is not divisible by 2, so we try the next smallest prime number, which is 3.

**Calculation:**
15 ÷ 3 = 5

**Step 5: Factor 5.**
Finally, we take 5, which is already a prime number.

**Summary of the factors:**
We have factored 120 as follows:
120 = 2 × 2 × 2 × 3 × 5

**Step 6: Write the prime factorization.**
We can express this in exponential form for clarity:
120 = 2^3 × 3^1 × 5^1

Thus, the prime factorization of 120 is:
**120 = 2^3 × 3 × 5**

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