Which composite number can divide the sum of the first 12 natural numbers?

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SSC CGL 2024 Tier-I Official Paper (Held On: 24 Sept, 2024 Shift 3)
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  1.  6
  2. 12
  3.  4
  4. 8

Answer (Detailed Solution Below)

Option 1 :  6
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Detailed Solution

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Given:

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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