The product of three consecutive numbers is always divisible by 6. True or False?
The correct option is A True
Yes, we can see that the above statement is true. Why is that so? Well, think about this:
In order for something to be divisible by 6, it must always be divisible by 3 and by 2.
In any set of three consecutive numbers (such as 1, 2, 3, or 24, 25, 26, etc) there will always be at least one even number, which means that the product of the numbers will be divisible by 2.
Also, since every third number is divisible by 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, etc), in a set of three consecutive numbers, one of the numbers will be divisible by 3, which means that the product of the three numbers will also be divisible by 3.
As we can see, the product of any three consecutive numbers will always be divisible by both 2 and 3, which then means that it will also always be divisible by 6.
Yes, we can see that the above statement is true. Why is that so? Well, think about this:
In order for something to be divisible by 6, it must always be divisible by 3 and by 2.
In any set of three consecutive numbers (such as 1, 2, 3, or 24, 25, 26, etc) there will always be at least one even number, which means that the product of the numbers will be divisible by 2.
Also, since every third number is divisible by 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, etc), in a set of three consecutive numbers, one of the numbers will be divisible by 3, which means that the product of the three numbers will also be divisible by 3.
As we can see, the product of any three consecutive numbers will always be divisible by both 2 and 3, which then means that it will also always be divisible by 6.
