Prime and Composite Numbers

  • An exact divisor of a number is called its factor.
  • The number 1 is a factor of every number.
  • Every number is a factor of itself.
  • The factors of a number are either less than or equal to the number itself.
  • All numbers have a finite number of factors.
  • The product of two numbers is called a multiple of each of the two numbers being multiplied.
  • A number is a multiple of all its factors.
  • Every number is a multiple of 1 and itself.
  • There are infinite multiples of a number.
  • Numbers that have only two factors in the form of 1 and the number itself are called prime numbers.
  • Numbers that have more than two factors are called composite numbers.
  • The number 1 is neither a prime number nor a composite number.
  • All number having 0, 2, 4, 6 or 8 in the unit‘s or one‘s place are multiples of 2 and are called even numbers.
  • All numbers having 1, 3, 5, 7 or 9 in the unit‘s place are called odd numbers.
  • The number 2 is the smallest prime number and also the only prime number that is even.
  • All prime numbers, except 2, are odd numbers.
  • The sum of any two prime numbers, except 2, is an even number.

Divisibility of Numbers

  • A number that has 0, 2, 4, 6 or 8 in its place is divisible by 2.
  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
  • A number that has 0 or 5 in its ones place is divisible by 5.
  • A number is divisible by 6 if that number is divisible by both 2 and 3.
  • A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
  • A number is divisible by 9 if the sum of its digit is divisible by 9.
  • A number that has 0 in its ones place is divisible by 10.
  • If the difference between the sum of digit at odd and even places in a given number is either 0 or a multiple of 11, then the given number is divisible by 11.
  • If a number is divisible by another number, then it is also divisible by all factors of the other number.
  • If two numbers are divisible by another number, then their sum and difference is also divisible by the other number.
  • If a number is divisible by two co-prime numbers, then it is also divisible by the product of the two co-prime numbers.
  • If the only common factor of two numbers is 1, then the two numbers are called co-prime numbers.

Prime Factorisation, HCF and LCM

  • Writing a number as a product of its prime factors is called prime factorization of the number.
  • The greatest common factor of given numbers is called their highest common factor (HCF).
  • The HCF of given numbers is equal to the product of their common prime factors in prime factorization.
  • The lowest common multiple of given numbers is called their Least Common Multiple (LCM).
  • The LCM of given number is equal to the product of their prime factors counted as the maximum number of times they occur in their prime factorization.


With our free PDF notes you can get success in any competitive or entrance exams like CTET,  KVS, NET, CAT, MAT, CMAT, SSC, B.ED, IBPS Recruitment, IAS, CSAT, State Civil Services Exams, UPTET, PSTET, HTET & many more. It also provides NCERT solutions, CBSE, NTSE, Olympiad study material, Indian General Knowledge, English, Hindi, Mathematics, Current affairs, Science, S.ST, model test papers, important Questions and Answers asked in CBSE examinations.

Post a Comment Blogger

 
Top