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Question

The number of proper divisors of 2p·6q·15r is equal to?


A

p+q+1(q+r+1)(r+1)

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B

p+q+1(q+r+1)(r+1)-2

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C

p+q(q+r)r-2

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D

None of these

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Solution

The correct option is B

p+q+1(q+r+1)(r+1)-2


Explanation for the correct option:

Find the number of proper divisors of the given number.

A number 2p·6q·15r is given.

Rewrite the given number as follows:

2p·6q·15r=2p·2·3q·3·5r2p·6q·15r=2p+q·3q+r·5r

So, the total number of divisors is (p+q+1)(q+r+1)(r+1).

since, 1 and the number itself is not included in proper divisors.

Therefore, the number of proper divisors is (p+q+1)(q+r+1)(r+1)-2.

Hence, option B is the correct option.


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