Question

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

Options

• 6

• 4

• 16

• 8

Answer 1

The greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1, is 4.

Explanation:

Let an odd natural number other than 1 be 3.

Then, predecessor of 3 = 3 – 1 = 2 and successor of 3 = 3 + 1 = 4

∴ Their product = 2 × 4 = 8

LCM of predecessor and successor i.e.

2	2, 4
2	1, 2
	1, 1

= 2 × 2

= 4

Hence, the greatest number which always divides the product of predecessor and successor of an odd natural number other than 1, is 4.