Write 98 as product of its prime factors.

Options

A. `2xx7^2`
B. `3xx7`
C. `5^2xx7`
D. `2^2xx7^2`

Answer

To write 98 as a product of its prime factors, we will follow these steps:

### Step 1: Divide by the smallest prime number
Start by dividing 98 by the smallest prime number, which is 2.

\[ 98 \div 2 = 49 \]

### Step 2: Factor the quotient
Next, we need to factor 49. Since 49 is not divisible by 2, we move to the next smallest prime number, which is 3.

\[ 49 \div 3 \quad \text{(not divisible)} \]

Next, we try 5:

\[ 49 \div 5 \quad \text{(not divisible)} \]

Now, we try 7:

\[ 49 \div 7 = 7 \]

### Step 3: Continue factoring
Now we have 7, which is also a prime number. So we can write:

\[ 7 \div 7 = 1 \]

### Step 4: Write the prime factorization
Now we can write the prime factorization of 98. We have:

\[ 98 = 2 \times 7 \times 7 \]

This can also be expressed using exponents:

\[ 98 = 2 \times 7^2 \]

### Final Answer
Thus, the prime factorization of 98 is:

\[ \boxed{2 \times 7^2} \]

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