Question

Which one of the following is the number by which
the product of 8 consecutive integers is divisible?
(a) 4 !
(b) 6 !
(c) 7!
(d) 8 !
(e) All of these​

Answer 1

Answer:

e) 4! , 6! , 7!  and 8!  all are  the numbers by which the product of 8 consecutive integers is divisible.

Step-by-step explanation:

Let the smallest number is n

then the product of 8 consecutive integers is  n, (n + 1), (n + 2), (n+3),---- (n + 7)

M= n, (n + 1), (n + 2), (n+3),---- (n + 7)

Put n = 1

m = 1  × 2  × 3 ,....  × 8 = 8 !

Not n = 2

m = 2 × 3 × 4, --------- × 9 = 9 ! = 9×8 !

The product of n natural numbers will be always divisible by n!.

So, all option are correct.