Hi Chaitanya,

The number of factors can also be calculated this way

Total calculated factors should be combination of (powers of 2 and powers of P with minimum power of 2 as 1 since every factor must be an even number)

2^1 P^0
2^2 P^1
____________________
2 values x 2 values = [spoiler]4 Factors Option-C[/spoiler]

The above method is based on the following method

For more information on number of factors calculation of any number, please refer to the below mentioned links.

https://www.cut-the-knot.org/blue/NumberOfFactors.shtml

https://www.wikihow.com/Find-How-Many-Fa ... n-a-Number

chaitanya.bhansali wrote:if n=4p, where p is a prime number greater than 2, how many DIFFERENT positive EVEN divisors does n have, including n?

A) 2
B) 3
C) 4
D) 6
E) 8

Probably the easiest way is to list them:

* 2
* 4
* 2p
* 4p

And you're done!

chaitanya.bhansali wrote:if n=4p, where p is a prime number greater than 2, how many DIFFERENT positive EVEN divisors does n have, including n?

A) 2
B) 3
C) 4
D) 6
E) 8

Solution:

This is an interesting question because we are immediately given the option to insert any prime number we wish for p, as long as it's greater than 2. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We want to work with small numbers if possible, so we can select 3 for p. Thus, we have:

n = 4 x 3

n = 12

Next we have to determine all the factors, or divisors, of p. Remember, the term "factor" is synonymous with the term "divisor."

1, 12, 6, 2, 4, 3

From this we see that we have 4 even divisors: 12, 6, 2, and 4.

If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let's say p = 5, so

n = 4 x 5

n = 20

The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.

In fact, no matter what the value of p is, as long as it is a prime number greater than 2, n will always have 4 even divisors.

The answer is C

Answer is C

all the prime number grtr than 2 are odd.

4 * odd number is even number which is multiple of 2,4,2n,4n so it will always be 4.