Question

1. The product of three consecutive integers is divisible by (a) 5 (6) 6 (c) 7 (d) none of these Please solve it giving solutions​

Answer 1

.

Consider the three consecutive numbers to be x,(x+1),(x+2)

.

For 2

:

If x

is not divisible by 2

, then it means that x

is odd.

Hence, if x

is odd, then it is a known fact that x+1

(any odd number plus 1

) is even, hence, is divisible by 2

.

Thus, out of the three consecutive numbers, at least one of them is always divisible by 2

.

For 3

:

Now, if a number is not divisible by 3

and is divided by it, then it can leave either of only two remainder – 1

and 2

.

If x

is not divisible by 3

and when divided by 3

leaves a remainder of 1

, then x+2

is going to be divisible by 3

.

If x

is not divisible by 3

and when divided by 3

leaves a remainder of 2

, then x+1

is going to be divisible by 3

.

Similarly, for the other two cases – (x+1)

and (x+2)

not being divisible by 3

, we can have that either of the other two are going to be divisible by 3

.

Thus, out of the three consecutive numbers, exactly one of them is always divisible by 3

.

Now, we have shown that out of the three consecutive numbers, one of them is always divisible by 2

and 3

. Hence, we showed that the product of any three consecutive numbers is always divisible by 6

So option b true

Make my answer as brainlist please

.