# 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 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 |

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 numbers LCM = 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 in the form |