# NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## CBSE Class 10 Math՚s Summary

This pdf list all the Class 10 CBSE math՚s formula in a concise manner to help the students in revision and examination as per NCERT syllabus

## Real Numbers

 S. no Type of Numbers Description 1 Natural Numbers It is the counting numbers 2 Whole number W It is the counting numbers + zero 3 Integers 4 Positive integers 5 Negative integers 6 Rational Number A number is called rational if it can be expressed in the form p/q where p and q are integers (q > 0) .Example: etc. 7 Irrational Number A number is called rational if it cannot be expressed in the form p/q where p and q are integers (q > 0) .Example: etc. 8 Real Numbers All rational and all irrational number makes the collection of real number. It is denoted by the letter R
 S. no Type of Numbers Description 1 Euclid՚s Division Lemma For a and b any two positive integer, we can always find unique integer q and r such that, If r = 0, then b is divisor of a. 2 HCF (Highest common factor) HCF of two positive integers can be find using the Euclid՚s Division Lemma algorithmWe know that for any two integers a, b. we can write following expression, If r = 0, thenHCF (a, b) = bIf , thenHCF (a, b) = HCF (b, r)Again expressing the integer b, r in Euclid՚s DivisionLemma, we getSimilarly successive Euclid՚s division can be writtenuntil we get the remainder zero, the divisor at thatpoint is called the HCF of the a and b 3 HCF (a, b) = 1 Then a and b are co primes. 4 Fundamental Theorem of Arithmetic Composite number = Product of primes 5 HCF and LCM by prime factorization method HCF = Product of the smallest power of each common factor in the numbersLCM = Product of the greatest power of each prime factor involved in the number 6 Important Formula Important concept for rational Number Terminating decimal expression can be written inthe form

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