Give the prime factorization of each of the following numbers :
48

Answer

To find the prime factorization of the number 48, we can follow these steps:

### Step 1: Start with the number 48
We begin with the number we want to factor, which is 48.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. We divide 48 by 2:
\[ 48 \div 2 = 24 \]

### Step 3: Continue dividing by 2
Next, we take the result (24) and divide it by 2 again:
\[ 24 \div 2 = 12 \]

### Step 4: Divide by 2 again
We continue the process with 12:
\[ 12 \div 2 = 6 \]

### Step 5: Divide by 2 one more time
Now we take 6 and divide it by 2:
\[ 6 \div 2 = 3 \]

### Step 6: Divide by the next prime number
Now we have 3, which is a prime number itself. We can stop here since we cannot divide 3 by 2 anymore.

### Step 7: Write down the prime factors
Now we can write down all the prime factors we used:
- We divided by 2 four times (2 x 2 x 2 x 2)
- We divided by 3 one time (3)

### Step 8: Combine the prime factors
Thus, the prime factorization of 48 can be expressed as:
\[ 48 = 2^4 \times 3^1 \]
or simply:
\[ 48 = 2 \times 2 \times 2 \times 2 \times 3 \]

### Final Answer:
The prime factorization of 48 is \( 2^4 \times 3^1 \).

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