CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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 $$1.$$

Mathematics
NCERT
Standard VI

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More



footer-image