To find the least number by which 23808 can be divided to get a perfect square quotient, we need to follow a step-by-step approach. In this response, we will explain the process in detail.



To find the least number, we need to follow these steps:

1. Find the prime factorization of the given number, 23808


2. Identify the factors that are not present in pairs


3. Make a product of these factors to get the least number to be divided

To find the prime factorization, we can use the following steps:

• Divide the given number by the smallest prime number, 2, until we can no longer divide by 2


• Divide the remaining quotient by the next prime number, 3, until we can no longer divide by 3


• Repeat this process with the next prime numbers until we have a quotient of 1

Using this method, we get:

23808 = 2 x 2 x 2 x 2 x 2 x 2 x 11 x 17



To identify the factors that are not present in pairs, we need to look for any prime factors that have an odd exponent. In this case, we have one factor with an odd exponent - 11.



To get the least number to be divided, we need to make a product of the factors that are not present in pairs. In this case, we only have one factor, 11. Therefore, the least number to be divided is:

2 x 2 x 2 x 2 x 2 x 2 x 11 = 5632

Therefore, when 23808 is divided by 5632, the quotient will be a perfect square.



In conclusion, to find the least number by which 23808 can be divided to get a perfect square quotient, we need to follow a step-by-step approach. We need to find the prime factorization of the given number, identify the factors that are not present in pairs, and make a product of these factors to get the least number to be divided. In this case, the least number to be divided is 5632.