Find the prime factorisation of:
5400

Options

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

Answer

To find the prime factorization of 5400, we will break it down into its prime factors step by step.

### Step 1: Divide by the smallest prime number
Start with the number 5400 and divide it by the smallest prime number, which is 2.

\[ 5400 \div 2 = 2700 \]

### Step 2: Continue dividing by 2
Since 2700 is still even, we can divide it by 2 again.

\[ 2700 \div 2 = 1350 \]

### Step 3: Divide by 2 again
1350 is also even, so we divide it by 2 once more.

\[ 1350 \div 2 = 675 \]

### Step 4: Switch to the next smallest prime number
Now, 675 is not even, so we switch to the next smallest prime number, which is 3.

\[ 675 \div 3 = 225 \]

### Step 5: Continue dividing by 3
225 is still divisible by 3, so we divide by 3 again.

\[ 225 \div 3 = 75 \]

### Step 6: Divide by 3 again
75 is also divisible by 3, so we divide by 3 once more.

\[ 75 \div 3 = 25 \]

### Step 7: Switch to the next smallest prime number
Now, 25 is not divisible by 3, so we switch to the next smallest prime number, which is 5.

\[ 25 \div 5 = 5 \]

### Step 8: Divide by 5 again
Finally, we divide 5 by itself.

\[ 5 \div 5 = 1 \]

### Step 9: Write the prime factorization
Now that we have reached 1, we can write the prime factorization of 5400. We collected the prime factors during our division:

\[ 5400 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \]

This can also be written in exponent form:

\[ 5400 = 2^3 \times 3^3 \times 5^2 \]

### Final Answer:
The prime factorization of 5400 is:

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

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