Find the HCF of 2800 and 756. 

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SSC GD Constable (2022) Official Paper (Held On : 30 Jan 2023 Shift 1)
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  1. 56
  2. 42
  3. 14
  4. 28

Answer (Detailed Solution Below)

Option 4 : 28
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Detailed Solution

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Given:

Two numbers 2800 and 756.

Concept:

The Highest Common Factor (HCF) can be found using the Euclidean Algorithm.

Solution:

Apply the Euclidean Algorithm:

⇒ 2800 = 3 × 756 + 532,

⇒ 756 = 1 × 532 + 224,

⇒ 532 = 2 × 224 + 84,

⇒ 224 = 2 × 84 + 56,

⇒ 84 = 1 × 56 + 28,

⇒ 56 = 2 × 28 + 0.

The last non-zero remainder is the HCF.

Therefore, the HCF of 2800 and 756 is 28.

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