Write the sum of exponents of prime factors in the prime factorisation of 250.

Options

A. 4
B. 6
C. 8
D. 3

Answer

To find the sum of the exponents of the prime factors in the prime factorization of 250, we can follow these steps:

### Step 1: Prime Factorization of 250
To begin, we need to perform the prime factorization of 250. We can start by dividing 250 by the smallest prime number, which is 2.

\[ 250 \div 2 = 125 \]

So, we have:

\[ 250 = 2 \times 125 \]

### Step 2: Factor 125
Next, we need to factor 125. The smallest prime number that can divide 125 is 5.

\[ 125 \div 5 = 25 \]

So, we can write:

\[ 125 = 5 \times 25 \]

### Step 3: Factor 25
Now we factor 25, which can also be divided by 5.

\[ 25 \div 5 = 5 \]

Thus, we have:

\[ 25 = 5 \times 5 \]

### Step 4: Combine the Factors
Now we can combine all the factors we have found:

\[ 250 = 2 \times 5 \times 5 \times 5 \]

This can be expressed in exponent form as:

\[ 250 = 2^1 \times 5^3 \]

### Step 5: Identify the Exponents
In the prime factorization \(2^1 \times 5^3\), the exponents of the prime factors are:
- The exponent of 2 is 1.
- The exponent of 5 is 3.

### Step 6: Sum of the Exponents
Now, we need to sum the exponents:

\[ 1 + 3 = 4 \]

### Final Answer
Thus, the sum of the exponents of the prime factors in the prime factorization of 250 is:

\[ \boxed{4} \]

---