The H.C.F of  $14,18,24$ is

The HCF, or Highest Common Factor, is the largest number that divides two or more numbers without leaving a remainder. To calculate the HCF of 14, 18, and 24, we will follow these steps:

Step 1: Prime Factorization

• The prime factors of 14 are: 2 × 7.
• The prime factors of 18 are: 2 × 3 × 3.
• The prime factors of 24 are: 2 × 2 × 2 × 3.

Step 2: Common Factors

From the prime factorization, we identify the common factors:

• 14 contains: 2
• 18 contains: 2
• 24 contains: 2

The only common prime factor among 14, 18, and 24 is 2.

Step 3: Verify with Smaller Pairs

Let's verify by calculating the HCF of 18 and 24:

• The prime factors of 18 are: 2 × 3 × 3.
• The prime factors of 24 are: 2 × 2 × 2 × 3.
• The common factors of 18 and 24 are: 2 and 3.

The product of the common factors (2 × 3) gives 6, which is the HCF of 18 and 24.

Step 4: Final Calculation

Returning to 14, 18, and 24, the only common factor among all three numbers is 2. Therefore, the HCF of 14, 18, and 24 is:

HCF = 2

Conclusion

By understanding the HCF of smaller pairs, such as the hcf of 18 and 24, and using prime factorization, we confirm that the HCF of 14, 18, and 24 is 2. Always remember, breaking down the problem into smaller parts like finding the hcf of 18 and 24 helps simplify the overall calculation.