5. What is th prime ractorization of 120 ?

Question

UpStudy AI · Accepted Answer

To find the **prime factorization** of **120**, we'll break it down into its prime components step by step.

### Step 1: Divide by the Smallest Prime Number (2)
120 is even, so we start by dividing by 2.

$$
120 ÷ 2 = 60
$$

### Step 2: Continue Dividing by 2
60 is also even.

$$
60 ÷ 2 = 30
$$

$$
30 ÷ 2 = 15
$$

Now, **2** is no longer a factor of 15.

### Step 3: Move to the Next Prime Number (3)
15 is divisible by 3.

$$
15 ÷ 3 = 5
$$

### Step 4: Finally, Divide by the Last Prime Number (5)
5 is a prime number.

$$
5 ÷ 5 = 1
$$

### Putting It All Together
The prime factors we used are:

$$
2 \times 2 \times 2 \times 3 \times 5
$$

This can be expressed using exponents as:

$$
2^3 \times 3 \times 5
$$

### **Prime Factorization of 120**

$$
120 = 2^3 \times 3 \times 5
$$
The prime factorization of 120 is $$2^3 \times 3 \times 5$$.

Real Tutor Solution