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The number of even divisors of the number N=12600=2332527 is
a. 72
b. 54
c. 18
d. None of these

Answer
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Hint: Here we are going to find prime factors and segregating all the factors into the even power and the odd power. Prime numbers are the whole number greater than 1 which cannot be made by multiplying other whole numbers. E.g. 2,3,5,7,....

Complete step by step solution:
On prime factorization, it consist of - 12600=23×32×52×7

According to general concept total number of factors in case of xn= (n+1)
Number of factors = (3+1)(2+1)(2+1)(1+1)
=72
Removing power of 2 keeping remaining factors which are odd is -
=(2+1)(2+1)(1+1)=(3)(3)(2)=18
As, total number of factors= the number of even factors + the number of odd factors
To get even factors we would subtract odd factors from the total number of factors.
Therefore, Even factors
=7218=54
Hence, the required answer is 54.

Therefore, option (B), 54 is correct.


Note: Prime factorization is finding which prime numbers multiply together to make the original number. Even numbers are 2,4,6,.... whereas odd numbers are 1,3,5,.... Remember 1 is neither prime nor composite. Always remember the difference between prime numbers (2,3,5....) and composite numbers (4,6,8,...) to solve factorization examples.
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