Create New Account
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Real Numbers

    Summary

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

10th class > Real Numbers > Summary

Summary

In this chapter, we have studied the following points:

The Fundamental Theorem of Arithmetic :

1. Every composite number can be expressed(factorised) as a product of , and this factorisation is , apart from the order in which the prime factors occur.

2. If p is a prime and p divides a2, then p divides a, where a is a integer.

We have learnt to prove that 2, 3 are .

NOTE FOR THE READER

You have seen that : HCF(p,q,r) × LCM(p,q,r) ≠ p × q × r, where p, q, r are positive integers (see Example 8). However, the following results hold good for three numbers p, q and r :

LCM (p, q, r) = p×q×r×HCFp,q,rHCFp,q×HCFq,r×HCFp,r

HCF (p, q, r) = p×q×r×LCMp,q,rLCMp,q×LCMq,r×LCMp,r