The sum of exponents of prime factors in the prime -factorisation of 196 is

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the sum of the exponents of the prime factors in the prime factorization of 196, we can follow these steps:

### Step 1: Prime Factorization of 196
To begin, we need to factor 196 into its prime factors.

1. Start with the number 196.
2. Divide by the smallest prime number, which is 2.
- \( 196 \div 2 = 98 \)
3. Now, factor 98.
- \( 98 \div 2 = 49 \)
4. Next, factor 49.
- \( 49 \div 7 = 7 \)
5. Finally, factor 7.
- \( 7 \div 7 = 1 \)

So, the complete factorization of 196 is:
\[ 196 = 2^2 \times 7^2 \]

### Step 2: Identify the Exponents
From the prime factorization, we can see the exponents of the prime factors:
- The exponent of 2 is 2.
- The exponent of 7 is 2.

### Step 3: Sum the Exponents
Now, we sum the exponents of the prime factors:
\[ 2 + 2 = 4 \]

### Final Answer
The sum of the exponents of the prime factors in the prime factorization of 196 is **4**.

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