Question

Find the HCF of 24 and 36.

• A. 6
• B. 12
• C. 18
• D. 24

Hint:

You can also find HCF by checking the difference. The HCF must be a factor of the difference between the numbers. $36 - 24 = 12$. Since 12 divides both 24 and 36, it is the HCF!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The HCF (Highest Common Factor) is the largest positive integer that divides each of the integers without leaving a remainder.

Step 2: Prime Factorization:
Find the prime factors of both numbers:
• $24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1$
• $36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2$

Step 3: Calculation:
To find the HCF, take the lowest power of the common prime factors:
• Common factor $2$: lowest power is $2^2 = 4$
• Common factor $3$: lowest power is $3^1 = 3$ \[ \text{HCF} = 4 \times 3 = 12 \]

Step 4: Final Answer:
The HCF of 24 and 36 is 12.