CBSE Class 10 Answered
The product of two consecutive positive integers is divisible by 6. Is this statement true or false? Justify your answer
Asked by KONDA VENKATA KHEERTHANA | 17 Apr, 2018, 07:36: PM
Expert Answer
Let y and y + 1 are consecutive numbers.
Product of two consecutive numbers is y(y + 1)
If y is even number then
y = 2k and y+1 = 2k + 1
2k(2k + 1) is divisible by 2.
Similarly if y is odd number then y = 2k + 1 and y + 1 = 2k + 2
then y(y + 1) = (2k + 1)(2k + 2) = 4k2 + 6k + 2 = 2(2k2 + 3k + 1)
Which is also divisible by 2.
Hence, The product of two consecutive positive integers is not divisible by 6.
Answered by Sneha shidid | 18 Apr, 2018, 09:18: AM
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