Find HCF by using the prime factor method: 54,81 and 99 .

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answer is B.

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Detailed Solution

Concept- To determine the HCF (Highest Common Factor) using the prime factor approach, you must first list the prime factors that each number has and then determine which prime factors are shared by all. Essentially, HCF is the sum of all the common factors among all the integers.
We are given the numbers 54, 81, and 99, and we must use the prime factor approach to get the HCF, or highest common factor.
Let's write all the numbers down and apply the prime factor method—which allows us to only utilize prime numbers as factors—to determine the HCF.
Let's start by determining the components of the number 54.

The right side must now be transformed into exponential form in order to obtain the result.

Here, in this

The number 3 denotes that it has been multiplied three times.
The prime factorization technique is the name of this approach.
Let's do the same thing by determining the prime factors for the integers 81 and 99.
For 81 , we get,

Let us do the same for the number 99 ,

Let's discover the common prime factors for all three numbers in the next phase., 54,81 and 99 .
From the numbers 54,81 and 99 the only common prime factor is

which is equal to 9 .
Thus, the HCF among the numbers 54,81 and 99 is 9
Hence, the correct answer is option 2.

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