Q. 304.0( 4 Votes )
The largest number which always divides the sum of any pair of consecutive odd numbers is
Sum of two consecutive numbers is always divisible by 4, for example
1 + 3 = 4
3 + 5 = 8
5 + 7 = 12
All are divisible by 4.
But 1 + 3 = 4 is neither divisible by 6 nor by 8, therefore 4 is the largest number which always divides the sum of any pair of consecutive odd numbers.
**Additional proof (Not for exam purpose)
Any two consecutive odd numbers will be in the form, 2n – 1 and 2n + 1, for n = 1, 2, 3, …and so on
Hence, their addition
2n – 1 + 2n + 1 = 4n is divisible by 4.
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