Give the prime factorization of each of the following numbers :
1323

Answer

To find the prime factorization of the number 1323, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start by dividing 1323 by the smallest prime number, which is 3.

1323 ÷ 3 = 441

### Step 2: Continue dividing by 3
Now, we will divide 441 by 3 again.

441 ÷ 3 = 147

### Step 3: Divide by 3 once more
Next, we will divide 147 by 3 again.

147 ÷ 3 = 49

### Step 4: Divide by the next smallest prime number
Now, we need to factor 49. The smallest prime number that can divide 49 is 7.

49 ÷ 7 = 7

### Step 5: Divide by 7 again
Finally, we divide 7 by itself.

7 ÷ 7 = 1

### Step 6: Write the prime factorization
Now, we can write the prime factorization of 1323. We divided by 3 three times and by 7 two times.

So, the prime factorization of 1323 is:

\[ 1323 = 3^3 \times 7^2 \]

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