Question

HCF of the numbers 49 and 91 will be :

• A. 7
• B. 9
• C. 11
• D. 13

Hint:

If you're stuck, use the long division method: $91 \div 49 = 1$ (rem 42); $49 \div 42 = 1$ (rem 7); $42 \div 7 = 6$ (rem 0). The last divisor (7) is the HCF.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Highest Common Factor (HCF) is the largest positive integer that divides each of the numbers without leaving a remainder. Prime factorization is a reliable method to find it.
Step 2: Prime Factorization:

$49 = 7 \times 7 = 7^2$
$91 = 7 \times 13$
Step 3: Identifying Common Factors:
The common prime factor in both numbers is $7$. The lowest power of $7$ present is $7^1$. $$\text{HCF} = 7$$
Step 4: Final Answer:
The HCF of 49 and 91 is 7.