The numbers of prime factors in `2^(222)xx3^(333)xx5^(555)` is-

Options

A. 3
B. 1107
C. 1110
D. 1272

Answer

To find the number of prime factors in the expression \(2^{222} \times 3^{333} \times 5^{555}\), we can follow these steps:

### Step 1: Identify the prime factors
The expression consists of three prime factors: \(2\), \(3\), and \(5\).

### Step 2: Count the occurrences of each prime factor
- The prime factor \(2\) appears \(222\) times.
- The prime factor \(3\) appears \(333\) times.
- The prime factor \(5\) appears \(555\) times.

### Step 3: Calculate the total number of prime factors
To find the total number of prime factors, we add the occurrences of each prime factor:
\[ 222 + 333 + 555 \]

### Step 4: Perform the addition
Now, we calculate the sum:
\[ 222 + 333 = 555 \]
\[ 555 + 555 = 1110 \]

### Final Answer
Thus, the total number of prime factors in the expression \(2^{222} \times 3^{333} \times 5^{555}\) is \(1110\).

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