Question

Let A and B be distinct positive integers such that each has the same number of
positive divisors that 2013 has. Compute the least possible value of A-B. Please answer thi quesion...This is urgent​

Answer 1

Answer:

1

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given Let A and B be distinct positive integers such that each has the same number of positive divisors that 2013 has. Compute the least possible value of A-B.

• Now we need to find the prime factors of 2013
• We get 3 x 11 x 61
• Also 2013 has 8 positive divisors.
• If A and B are distinct positive integers then mod A – B >= 1.
• Now a positive integer which has 8 divisors will be of the form a^7, a^3b or abc where a,b,c are distinct prime numbers.
• So if b is a prime number greater than 2 then each number of the form 8b will have 8 positive divisors.
• Those numbers will be 24 40 56 88 104 136.
• Apart from these numbers if we factorize 105 we get the factors as 3 x 5 x 7. So both 104 and 105 have 8 positive divisors.
• Therefore we get A = 104 and B = 105 and so mod A – B = 1

Reference link will be

https://brainly.in/question/16324336