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

Real Numbers
S. noType of NumbersDescription
1Natural Numbers

It is the counting numbers

2Whole numberW

It is the counting numbers + zero

4Positive integers
5Negative integers
6Rational NumberA number is called rational if it can be expressed in the form p/q where p and q are integers (q > 0) .

Example: etc.

7Irrational NumberA number is called rational if it cannot be expressed in the form p/q where p and q are integers (q > 0) .

Example: etc.

8Real NumbersAll rational and all irrational number makes the collection of real number. It is denoted by the letter R
S. No Type of Numbers Description
S. noType of NumbersDescription
1Euclid՚s Division LemmaFor 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.

2HCF (Highest common factor)HCF of two positive integers can be find using the Euclid՚s Division Lemma algorithm

We know that for any two integers a, b. we can write following expression


If r = 0, then

HCF (a, b) = b

If , then

HCF (a, b) = HCF (b, r)

Again expressing the integer b, r in Euclid՚s Division

Lemma, we get

Similarly successive Euclid՚s division can be written

until we get the remainder zero, the divisor at that

point is called the HCF of the a and b

3HCF (a, b) = 1Then a and b are co primes.
4Fundamental Theorem of ArithmeticComposite number = Product of primes
5HCF and LCM by prime factorization methodHCF = Product of the smallest power of each common factor in the numbers

LCM = Product of the greatest power of each prime factor involved in the number

6Important Formula
Important concept for rational NumberTerminating decimal expression can be written in

the form

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