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Consider the natural number n=453600. ...

Consider the natural number n=453600.
Statement-1: The number of divisors of n is 180.
Statement-2: The sum of the divisors of n is
`((2^(6)-1)(3^(5)-1)(5^(3)-1)(7^(2)-1))/(48)`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

AI Generated Solution

To solve the problem, we need to verify both statements regarding the natural number \( n = 453600 \). ### Step 1: Prime Factorization of \( n \) First, we need to find the prime factorization of \( n \). 1. Start by dividing \( n \) by the smallest prime number, which is 2. \[ ...
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