Question

Let S(n) represents the sum of digits of a natural number n. For example, S(128)=1+2+8=11. What is the value of \(S( 2^6\times3^4\times5^5 )\)?

• A. 9
• B. 11
• C. 14
• D. 10

Answer 1

The Correct Option is A

To find the value of \( S(2^6 \times 3^4 \times 5^5) \), we first need to calculate the expression \( 2^6 \times 3^4 \times 5^5 \) numerically.

1. Calculate each power:
   • \( 2^6 = 64 \)
   • \( 3^4 = 81 \)
   • \( 5^5 = 3125 \)
2. Now, compute the product:
   • First calculate \( 64 \times 81 \):
     • \( 64 \times 81 = 5184 \)
   • Then multiply by 3125:
     • \( 5184 \times 3125 = 16200000 \)
3. Now, find the sum of the digits of 16200000:
   • \( S(16200000) = 1 + 6 + 2 + 0 + 0 + 0 + 0 + 0 = 9 \)

Therefore, the sum of the digits, \( S(2^6 \times 3^4 \times 5^5) \), is 9.