Question

The product of natural number and its successor is always divisible by
​

Answer 1

Let us take some examples
Example 1: Natural Number : 5
Successor : 6
Product of 5 and 6 = 5x6 = 30
Example 2: Natural Number : 9
Successor : 10
Product of 9 and 10 = 9x10 = 90

=> We can take uncountable exposes of the product of a natural number and it’s successor but the product will always be an even number ( a number ending with 0,2,4,6 or 8) . ( You may try any combination of a natural number and it’s successor )
We all know that all the natural even numbers in the number system are a multiple of 2 ( that means every natural even number is fully divisible by 2 and leaves no remainder on being divided by 2)

Thus we can safely conclude that the product of natural number and it’s successor is always divisible by 2.

P.S. The answer can also be 1 as it is a universal divisor ( that means it can divide any number ) but as the quotient when divided by 1 remains the same as the dividend( the number which is divided ) 1 is not a suitable answer to this question .