
The number of even divisors of the number is
a. 72
b. 54
c. 18
d. None of these
Answer
500.1k+ views
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.
Complete step by step solution:
On prime factorization, it consist of -
According to general concept total number of factors in case of = (n+1)
Number of factors =
Removing power of 2 keeping remaining factors which are odd is -
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
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 whereas odd numbers are Remember 1 is neither prime nor composite. Always remember the difference between prime numbers and composite numbers to solve factorization examples.
Complete step by step solution:
On prime factorization, it consist of -
According to general concept total number of factors in case of
Number of factors =
Removing power of 2 keeping remaining factors which are odd is -
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
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
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