Question

find the greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1

Answer 1

Answer:
The greatest number which always divide the product of the predecessor and successor of an odd natural number other than ' 1 '  is

let odd number = 3 , So product of predecessor and successor  = 2 × 4 = 8
And another odd number = 5 so product of predecessor and successor  = 4 × 6 = 24

To find the greatest number we  find H.C.F. of 8 and 24 

8 = 2× 2 × 2
24 = 2 × 2 × 2 × 3
So,
H.C.F. ( 8 , 24 )   = 2 × 2 × 2    = 8                        

greatest number which always divide the product of the predecessor and successor of an odd natural number other than ' 1 '  is

= 8               ( Ans )

Answer 2

Hey mate.
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First of all,

We will take the odd number 3 ,

So product of predecessor and successor

 = 2 × 4

= 8

And then, The other odd number 5

So,

The product of predecessor and successor

 = 4 × 6

= 24

In order to find the greatest number we  find the H.C.F. of 8 and 24 

8 = 2× 2 × 2

24 = 2 × 2 × 2 × 3

So,

H.C.F. ( 8 , 24 )   = 2 × 2 × 2   = 8                        

Thus , The greatest number which always divide the product of the predecessor and successor of an odd natural number other than ' 1 '  is 8   

Hope it helps !!!