Question

What is the HCF of 24 and 36?

• A. 6
• B. 12
• C. 18
• D. 24

Hint:

For HCF, use prime factorization and take the lowest power of each common prime.

Answer 1

The Correct Option is B

- Step 1: Find prime factors. 24 = 2^3 \times 3, 36 = 2^2 \times 3^2.
- Step 2: Calculate HCF. HCF = lowest powers of common primes = 2^2 \times 3 = 4 \times 3 = 12.
- Step 3: Verify. Check divisibility: 24 \div 12 = 2, 36 \div 12 = 3. Both are integers.
- Step 4: Check options. Options: (1) 6, (2) 12, (3) 18, (4) 24. HCF = 12 matches option (2).
- Step 5: Conclusion. Option (2) is correct.