Let's assume the three consecutive positive integers as x, x+1, and x+2.
Given that the product of these three integers is 15600, we can form the equation:
x * (x+1) * (x+2) = 15600

To solve this equation, we can start by finding the prime factorization of 15600:
15600 = 2^4 * 3 * 5^2 * 13

Now, let's equate the prime factorization of the equation:
x * (x+1) * (x+2) = 2^4 * 3 * 5^2 * 13

From the prime factorization, we can see that the prime factors on the right side of the equation are 2, 3, 5, and 13. To form the product of three consecutive integers, we need to distribute these prime factors among the three integers in a way that their product is equal to the right side of the equation.

We can start by distributing the prime factor 2 among the three integers. Since the consecutive integers have a difference of 1, one of the integers must be divisible by 2. Therefore, either x or x+1 must be divisible by 2. We can write the possibilities as:
1) x is divisible by 2
2) x+1 is divisible by 2

Case 1: x is divisible by 2
If x is divisible by 2, then we can write x as 2k, where k is a positive integer. Substituting this into the equation, we have:
(2k) * (2k+1) * (2k+2) = 2^4 * 3 * 5^2 * 13

Simplifying this equation, we get:
4k(k+1)(2k+1) = 2^4 * 3 * 5^2 * 13

Dividing both sides of the equation by 4, we have:
k(k+1)(2k+1) = 2^3 * 3 * 5^2 * 13

Now, we can see that k, (k+1), and (2k+1) are three consecutive integers. We can distribute the remaining prime factors among these integers.

Case 2: x+1 is divisible by 2
If x+1 is divisible by 2, then we can write x+1 as 2k, where k is a positive integer. Substituting this into the equation, we have:
(2k-1) * 2k * (2k+1) = 2^4 * 3 * 5^2 * 13

Simplifying this equation, we get:
4k(k-1)(2k+1) = 2^4 * 3 * 5^2 * 13

Dividing both sides of the equation by 4, we have:
k(k-1)(2k+1) = 2^3 * 3 * 5^2 * 13

Now, we can see that (k-1), k, and (2k+1) are three consecutive integers. We can distribute the remaining prime factors among these integers.

By solving these two cases, we can find the three consecutive positive integers and

Here, 15600= 2*2*3*2*2*13*5*5
3 consecutive number only have 5 as a factor in only 1 number.
so let aside all 5 which give us= 5*5= 25.
now by closely examining the above factors, we can form 2*2*2*3=24 & 13*2= 26 around number 25.

so, 24,25 & 26 are our three cons. int. now you are good to go.