Mathematics · Class 10

Euclid’s Division Lemma

Mathematics · Class 10 · Free concept lesson

1. Introduction: Sharing Without Leftovers... or With

You already know how to divide. You have been doing it since Class 4.

But here is a question you may not have thought about. When you divide 23 by 5, you get a quotient of 4 and a remainder of 3. You can write it as:

23 = 5 × 4 + 3

Now think about this. Is there any pair of whole numbers where this kind of writing breaks down? Can you always write a number as "divisor times quotient plus remainder"?

That is what this section is about. We are going to look at a rule that has been around for over 2,000 years. It is named after a Greek mathematician called Euclid. And it turns out to be the foundation for finding HCF, which you will need in the very next section.


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