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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
Solution
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.
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