real numbers concepts Class 10 Mathematics, terms and formulas | HCF LCM...

EDUCATION WIZ Class 10 Mathematics Chapter 1 Real Numbers important Terms, Concepts and Formulas (For Board Exam 2025-26) 

 

1. Natural Numbers N = {1,2,3,4,.......} 

 2. Whole Numbers W = {0,1,2,3,.......} 

 3. Integers Z = {...-2,-1,0,1,2...} 

 4. Rational Nos R = {-1/3, 4/5, 0, -5, 8} expressible in p/q form where p and q are integers q ≠ 0 

 5. Irrational Numbers are the numbers which are not rational numbers. (not expressible in p/q form where p and q are integers q ≠ 0 Eg 2.234646788......., π, √2, √3 

 6. Real Numbers :- the set of rational numbers and irrational numbers 

 7. Prime numbers:- Number having exactly two factors. Eg 2,3,5,7,11,13,17 etc 

 8. Smallest Prime number is 2 

 9. Only Even Prime numbers is 2 

 10. The smallest Odd Prime number is 3. 

 11. Composite Numbers :- Number having more than two factors Eg 4, 6, 8,9,10 etc 

 12. Smallest composite number is 4 

 13. Smallest Odd composite number is 9 

 14. 1 is neither prime nor composite. It is called unique number 

 15. Perfect Square or Square numbers 1,4,9,16,25,36,49,64,81,100 and so on 

 16. FUNDAMENTAL THEOREM OF ARITHMETIC Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. 

 17. HCF by Prime factorisation method: Take the smallest power of common prime factors. Eg:- P=a³b⁴ and Q=a⁴b Then HCF (P and Q) = a³b 

 18. LCM by Prime factorisation method :- Take the largest power of common prime factors. Eg:- P=a³b⁴ and Q=a⁴b Then LCM (P and Q) = a⁴b⁴ 

 19. For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b. 

 20. HCF of two co-prime no is 1 and their LCM is their product 

 21. HCF of two numbers is always the factor of Their LCM i.e. LCM is exactly divisible by HCF. 

 22. Theorem 1.4 : √2 is irrational (Revise its proof NCERT page no 12)