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Q.

The total number of even factors in N is, if Question Image.


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a

134

b

248

c

25

d

144 

answer is D.

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Detailed Solution

Concept- With the use of the provided number's prime factors, we will first determine the total number of factors. The odd factors will next be subtracted from the total number of factors in order to determine the even factors of N. We will therefore have an even number of components.
Given that
Question ImageCurrently, 3 and 5 are prime numbers, but 12 is not. So let's represent it as a prime number product.
Question ImageYes, all of the numbers are now in excellent shape. Let's now reorganise their powers.
Question ImageThe powers of terms with the same base must be added.
Question ImageHere, we find the last base with their abilities. But the issue hasn't been resolved yet! The complete number of N's factors will now be determined.
The form of N that we have is Question Image.
And the formula for total factor numbers is Question Image.
By doing so, we obtain the following numbers:
Question ImageHowever, since we only want the even factors,we must take the odd factors out. Now that 3 and 5 are combined, we have the odd factors. Let's thus take their variables out.
Question ImageFinally, there are 144 even factors in all.
Hence, option 4 is correct.
 
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