Find the prime factorisation of:
3024

Options

A. `2 xx 2 xx 2xx 3 xx 3 xx 3 xx 3xx 7`
B. `2 xx 2 xx 2xx 2 xx 3 xx 3 xx 3xx 7`
C. `2 xx 2 xx 2xx 2 xx 3 xx 3 xx 3xx 11`
D. `2 xx 2 xx 2xx 2 xx 3 xx 3 xx 3xx 5`

Answer

To find the prime factorization of 3024, we will follow these steps:

### Step 1: Start with the number 3024
We begin with the number 3024 and look for the smallest prime number that can divide it. Since the last digit of 3024 is 4, it is even, and we can start with 2.

### Step 2: Divide by 2
Divide 3024 by 2:
- 3024 ÷ 2 = 1512

### Step 3: Continue dividing by 2
Now, we continue dividing by 2:
- 1512 ÷ 2 = 756
- 756 ÷ 2 = 378
- 378 ÷ 2 = 189

At this point, 189 is not divisible by 2 anymore since it is odd.

### Step 4: Move to the next prime number, which is 3
Now we divide 189 by 3:
- 189 ÷ 3 = 63

### Step 5: Continue dividing by 3
We continue dividing by 3:
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7

### Step 6: 7 is a prime number
Now we have reached 7, which is a prime number and cannot be divided further.

### Step 7: Write down the prime factors
Now we can write down all the prime factors we used:
- From our divisions, we have used 2 four times and 3 three times, and 7 once.

### Step 8: Express the prime factorization
Thus, the prime factorization of 3024 can be expressed as:
- \( 2^4 \times 3^3 \times 7^1 \)

### Final Answer
The prime factorization of 3024 is \( 2^4 \times 3^3 \times 7^1 \).

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