For what prime number p in the number 3785p so that the number is exactly divisible by 3?
For what prime number p in the number 3785p so that the number is exactly divisible by 3?
संख्या 3785p में कौन सी अभाज्य संख्या p होनी चाहिए कि संख्या 3 से पूर्णतः विभाज्य हो?
Detailed Solution & Logic
Correct Answer:
7
Solution
For a number to be divisible by 3, the sum of its digits must be divisible by 3.
For 3785p:
$3 + 7 + 8 + 5 + p = 23 + p$
The possible prime digits are $2, 3, 5, 7$.
Checking:
- 23 + 2 = 25 ❌
- 23 + 3 = 26 ❌
- 23 + 5 = 28❌
- 23 + 7 = 30 ✅
Therefore,
p = 7
Answer: 7 ✅
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