The H.C.F of 18 and 60 with solution

Finding the Highest Common Factor (H.C.F) of two numbers involves determining the largest number that can divide both given numbers without leaving any remainder. In this case, we need to find the H.C.F of 18 and 60.

Prime Factorization Method:
To find the H.C.F using the prime factorization method, we need to express both numbers as a product of their prime factors.

Prime Factorization of 18:
18 can be expressed as 2 * 3^2, where 2 and 3 are prime numbers.

Prime Factorization of 60:
60 can be expressed as 2^2 * 3 * 5, where 2, 3, and 5 are prime numbers.

Identifying Common Prime Factors:
To find the H.C.F, we need to identify the common prime factors between 18 and 60. In this case, the common prime factors are 2 and 3.

Taking the Smallest Powers:
Now, we need to take the smallest powers of the common prime factors, which are 2^1 and 3^1.

Multiplying the Common Prime Factors:
Finally, we multiply the common prime factors with their smallest powers. In this case, the H.C.F of 18 and 60 is 2^1 * 3^1 = 2 * 3 = 6.

Therefore, the H.C.F of 18 and 60 is 6.

Conclusion:
Using the prime factorization method, we determined that the H.C.F of 18 and 60 is 6. This means that 6 is the largest number that can divide both 18 and 60 without leaving any remainder.