Find the prime factorisation of:
4536

Options

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

Answer

To find the prime factorization of the number 4536, we will follow a systematic approach by dividing the number by the smallest prime numbers until we reach 1. Here are the steps:

### Step 1: Start with the number 4536
We will begin by writing down the number we want to factorize:
- **4536**

### Step 2: Divide by the smallest prime number (2)
Since 4536 is an even number, it is divisible by 2. Let's divide:
- **4536 ÷ 2 = 2268**
- Write down the quotient: **2**

### Step 3: Divide again by 2
Now we will divide 2268 by 2 again:
- **2268 ÷ 2 = 1134**
- Write down the quotient: **2**

### Step 4: Divide again by 2
We will continue dividing by 2:
- **1134 ÷ 2 = 567**
- Write down the quotient: **2**

### Step 5: Divide by the next smallest prime number (3)
Now, 567 is not even, so we try dividing by the next smallest prime number, which is 3:
- **567 ÷ 3 = 189**
- Write down the quotient: **3**

### Step 6: Divide by 3 again
Next, we divide 189 by 3:
- **189 ÷ 3 = 63**
- Write down the quotient: **3**

### Step 7: Divide by 3 again
Continue dividing by 3:
- **63 ÷ 3 = 21**
- Write down the quotient: **3**

### Step 8: Divide by 3 again
We divide 21 by 3:
- **21 ÷ 3 = 7**
- Write down the quotient: **3**

### Step 9: Divide by the next prime number (7)
Finally, we are left with 7, which is a prime number:
- **7 ÷ 7 = 1**
- Write down the quotient: **7**

### Step 10: Write the prime factorization
Now we can write the prime factorization of 4536 by combining all the prime factors we have found:
- **4536 = 2 × 2 × 2 × 3 × 3 × 3 × 7**
- This can also be written in exponential form as:
- **4536 = 2^3 × 3^3 × 7**

### Summary of the Prime Factorization
The prime factorization of 4536 is:
- **2^3 × 3^3 × 7**

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