Question

# What is the HCF of two consecutive odd numbers?

Solution

## Let those numbers be $$2n−1$$ and $$2n+1$$. Then the equation$$n(2n−1)−(n−1)(2n+1)=1$$holds true, as you can check by expanding the terms.Which means that 1 is an integer linear combination of the two consecutive numbers, hence their highest common factor is $$1$$: a number that divides $$2n−1$$ and $$2n+1$$ obviously divides the left hand side of the equation. Then it also divides the right hand side of the equation, which is $$1.$$MathematicsNCERTStandard VI

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