The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 248 and 492, we can use the Euclidean algorithm, which is efficient and straightforward.

Step 1: Divide the larger number by the smaller number and find the remainder.

Here, 492 is larger than 248. So, divide 492 by 248:

$492 \div 248 = 1 (quotient) with remainder 492 - (248 \times 1) = 492 - 248 = 244$

So, remainder is 244.

Step 2: Now, replace the larger number (492) with the smaller number (248), and the smaller number with the remainder (244). So, we now find HCF of 248 and 244.

Divide 248 by 244:

$248 \div 244 = 1 (quotient) with remainder 248 - (244 \times 1) = 248 - 244 = 4$

So, remainder is 4.

Step 3: Replace the larger number (248) with the smaller number (244), and the smaller number with the remainder (4). So, we now find HCF of 244 and 4.

Divide 244 by 4:

$244 \div 4 = 61 (quotient) with remainder 244 - (4 \times 61) = 244 - 244 = 0$

Since the remainder is 0, the divisor at this step, which is 4, is the HCF.

Final Answer: The HCF of 248 and 492 is $4$ .

Related Topics and Formulae

Euclidean Algorithm: This is a method to find the HCF of two numbers by repeatedly applying the division algorithm. The process continues until the remainder becomes zero. The divisor at this final step is the HCF.

Formula: If $a$ and $b$ are two numbers, and $a = b q + r$ , then $HCF (a, b) = HCF (b, r)$ .

Prime Factorization: Another method to find HCF is by expressing both numbers as a product of their prime factors. The HCF is then the product of the smallest power of all common prime factors.