Give the prime factorization of each of the following numbers :
1035

Answer

To find the prime factorization of the number 1035, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start by dividing 1035 by the smallest prime number, which is 3.

\[ 1035 \div 3 = 345 \]

### Step 2: Continue dividing by 3
Now, we will divide 345 by 3 again since it is still divisible by 3.

\[ 345 \div 3 = 115 \]

### Step 3: Divide by the next smallest prime number
Next, we will divide 115 by the next smallest prime number, which is 5.

\[ 115 \div 5 = 23 \]

### Step 4: Divide by the next smallest prime number
Now, we will divide 23 by itself since it is a prime number.

\[ 23 \div 23 = 1 \]

### Step 5: Write the prime factorization
Now that we have reached 1, we can write the prime factorization of 1035. The prime factors we found are:

\[ 3, 3, 5, 23 \]

We can express this as:

\[ 3^2 \times 5^1 \times 23^1 \]

### Final Answer
The prime factorization of 1035 is:

\[ 3^2 \times 5 \times 23 \]

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