Find the prime factorisation of:
`504`

Options

A. `2 xx 2 xx 3 xx 3 xx 3 xx 7`
B. `2 xx 2 xx 2 xx 3 xx 3 xx 7`
C. `2 xx 2 xx 2 xx 3 xx 3 xx 6`
D. `2 xx 2 xx 3 xx 3 xx 3 xx 6`

Answer

To find the prime factorization of 504, we will divide the number by the smallest prime numbers until we reach 1. Here are the steps:

### Step 1: Start with the number 504
We begin with the number 504.

### Step 2: Divide by the smallest prime number (2)
Since 504 is even, we can divide it by 2:
\[ 504 \div 2 = 252 \]
So, we have one factor of 2.

### Step 3: Continue dividing by 2
Next, we take 252, which is also even, and divide it by 2 again:
\[ 252 \div 2 = 126 \]
Now, we have two factors of 2.

### Step 4: Divide 126 by 2
We continue with 126, which is again even:
\[ 126 \div 2 = 63 \]
Now, we have three factors of 2.

### Step 5: Move to the next smallest prime (3)
Now we have 63, which is not even. We check the next smallest prime number, which is 3:
\[ 63 \div 3 = 21 \]
Now, we have one factor of 3.

### Step 6: Divide 21 by 3
Next, we take 21 and divide it by 3 again:
\[ 21 \div 3 = 7 \]
Now, we have two factors of 3.

### Step 7: Divide 7 by itself
Finally, we take 7, which is a prime number, and divide it by 7:
\[ 7 \div 7 = 1 \]
Now, we have one factor of 7.

### Step 8: Compile the prime factors
Now, we can compile all the prime factors we found:
- Factors of 2: 2, 2, 2 (or \(2^3\))
- Factors of 3: 3, 3 (or \(3^2\))
- Factor of 7: 7 (or \(7^1\))

### Final Result
The prime factorization of 504 is:
\[ 504 = 2^3 \times 3^2 \times 7^1 \]

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