Write the prime factorisation of the greatest 3-digit number.

Options

A. 3 times 3 times 3 times 37`
B. 2 times 3 times 3 times 37`
C. 2 times 3 times 3 times 37`
D. None of these

Answer

To find the prime factorization of the greatest 3-digit number, we can follow these steps:

### Step 1: Identify the greatest 3-digit number
The greatest 3-digit number is 999.

### Step 2: Start the prime factorization
We will begin by dividing 999 by the smallest prime number, which is 3.

### Step 3: Divide 999 by 3
- 999 ÷ 3 = 333

### Step 4: Continue dividing by 3
Next, we take 333 and divide it by 3 again.
- 333 ÷ 3 = 111

### Step 5: Divide 111 by 3
Now, we take 111 and divide it by 3 once more.
- 111 ÷ 3 = 37

### Step 6: Check if 37 is a prime number
The number 37 is a prime number, meaning it cannot be divided further by any prime number other than itself.

### Step 7: Write the prime factorization
Now we can write the prime factorization of 999:
- 999 = 3 × 3 × 3 × 37
- This can also be expressed in exponential form as \(3^3 \times 37\).

### Final Answer
The prime factorization of the greatest 3-digit number (999) is \(3^3 \times 37\).

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