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

Let a be a odd natural number

Predecessor (number before) = a - 1 = 2× b (a even number)

Successor (number after) = a+1 = 2× c (a even number)

Since,

The product of the predecessor and successor of an odd natural n

= (2× b) × (2× c)

= 4× b× c

Hence, the largest dividing number is 4