Question
Download Solution PDFWhich composite number can divide the sum of the first 12 natural numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
First 12 natural numbers = 1, 2, 3, ..., 12
Formula used:
Sum of first n natural numbers = \(\frac{n(n+1)}{2}\)
Calculations:
Sum of first 12 natural numbers = \(\frac{12(12+1)}{2} = \frac{12 \times 13}{2} = 78\)
⇒ Sum = 78
Now, we check which composite number divides 78.
78 ÷ 6 = 13
⇒ 6 divides 78 perfectly.
Conclusion:
The composite number that divides the sum of the first 12 natural numbers is 6.
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