The H.C.F. of $3556$ and $3444$ is

### Concept & Strategy To find the Highest Common Factor (HCF) of two large numbers quickly, use the **Difference Method**. The fundamental rule states that the HCF of two numbers divides their difference. Therefore, the HCF is either the difference itself or a factor of that difference. ### Step-by-Step Solution * **Given:** We need to find the HCF of $3556$ and $3444$. * **Step 1:** Calculate the difference between the two numbers. $$3556 - 3444 = 112$$ * **Step 2:** The HCF must be a factor of $112$. Let's test the given options against the number $112$. * $112 \div 23 \approx 4.86$ (Not a factor) * $112 \div 25 = 4.48$ (Not a factor) * $112 \div 26 \approx 4.30$ (Not a factor) * $112 \div 28 = 4$ (Exact factor!) * **Step 3:** Since $28$ is the only option that cleanly divides the difference ($112$), it must be the HCF. (Both $3556$ and $3444$ are divisible by $28$). ### Exam Strategy & Shortcut Take the difference ($112$). Scan the options and look at the unit digits. To get a unit digit of $2$ in $112$, multiplying by a number ending in $8$ ($28 \times 4$) is the most logical step. This saves you from having to test divisibility for every single option. ### Common Pitfall Using the continuous long division method for finding the HCF here will work, but it consumes valuable time during an exam. Relying on primary school methods instead of competitive aptitude shortcuts (like the difference rule) is the biggest reason students fail to finish quantitative sections on time. ### Final Answer **Therefore, the correct answer is 28.**