denotes that is a divisor of b, but is not a divisor of b for the positive integers a, b, and k. Find the value of k if k is a positive integer and ?

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answer is B.

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Detailed Solution

Concept- We begin by factoring the numbers up to the point where they can no longer be further divided by any prime number. We then determine the greatest power of 2 that can divide 72 in half, which informs us that the next power of 2 is unable to divide 72. The value of k is then determined by comparing the calculated power of 2 with

.
The problem states that for the positive integers a, b, and k,

signifies that

is a divisor of b, but

is not a divisor of b. If

is provided, then we must determine the value of k.
Let's start by factorising 72 to determine the highest value of

that can divide 72 in half.
So, we know that

We can see that the largest power of two that may divide 72 entirely is

, which divides 72 exactly.
Thus,

cannot be divided by 72.
By comparing

with

, we may determine that k is equal to 3. k has a value of 3.
Hence, option 2 is correct.

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