Give the prime factorization of `1260` .

Options

A. `2 xx 3 xx 3 xx 5 xx 7`
B. `2 xx 2 xx 3 xx 3 xx 5 xx 7`
C. `2 xx 2 xx 5 xx 7`
D. none of these

Answer

To find the prime factorization of 1260, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start by dividing 1260 by the smallest prime number, which is 2 (since 1260 is even).

\[ 1260 \div 2 = 630 \]

### Step 2: Continue dividing by 2
Now, we continue dividing by 2 since 630 is also even.

\[ 630 \div 2 = 315 \]

### Step 3: Move to the next smallest prime number
Next, we check 315. It is not divisible by 2 (since it's odd), so we move to the next smallest prime number, which is 3.

\[ 315 \div 3 = 105 \]

### Step 4: Divide by 3 again
Now, we divide 105 by 3 again.

\[ 105 \div 3 = 35 \]

### Step 5: Move to the next smallest prime number
Next, we check 35. It is not divisible by 3, so we move to the next prime number, which is 5.

\[ 35 \div 5 = 7 \]

### Step 6: Divide by 7
Finally, we divide by 7, which is also a prime number.

\[ 7 \div 7 = 1 \]

### Step 7: Write the prime factorization
Now we can write the prime factorization of 1260 using the prime numbers we divided by:

\[ 1260 = 2 \times 2 \times 3 \times 3 \times 5 \times 7 \]

This can also be written in exponential form as:

\[ 1260 = 2^2 \times 3^2 \times 5^1 \times 7^1 \]

### Final Answer:
The prime factorization of 1260 is \( 2^2 \times 3^2 \times 5^1 \times 7^1 \).

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