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Properties of Natural Numbers Addition Properties of Natural Numbers: 1. Closure Property:   The sum of two natural numbers is always a natural numbers. Example: Let two natural numbers 2 and 5 then                            2 + 5 = 7 is a natural number. 2. Commutative Property: Let a and b are two natural numbers,                                                a + b = b + a  Example: Let two natural numbers are 5 and 7 then                   5 + 7 = 12                   7 + 5 = 12   then        5 + 7 = 7 + 5  Hence commutative property is verified 3. Associative Property:   Let a, b and c are three natural numbers,                                             a + ( b + c) = (a + b ) + c Example: Let three natural numbers are 3, 5 and 6 then                   3 + ( 5 + 6 ) = 3 + 11 = 14                   (3 + 5 ) + 6  =  8 + 6  = 14  then          3 + ( 5 + 6 ) =   (3  + 5 )  + 6  Hence Associative property is verified 4. Existence of Additive Identity:

Natural Numbers Counting numbers are known as natural numbers.  It is denoted by "N"  N = { 1,2,3,4,5,6,7,8,9,10,11,12,13, ....... } Type of Natural numbers  1. Prime numbers  2. Composite numbers   1. Prime numbers A number which have only two prime factor, it is called a prime numbers. It is denoted by "P".  P = { 2,3,5,7,11,13,17,19, ....... } e.g. "2" have two factors 1 and itself .  Similarly some other examples written below :                     3 -> 1 and 3                     5 -> 1 and 5                     7 -> 1 and 7                                                      11 -> 1 and 11 etc.  2. Composite numbers A numbers which have more than two factors, it is called a composite numbers.      { 4,6,8,9,10,12,14,15,16,18, ...... } e.g. "4" have more than two factors 1, 2 and 4 Similarly some other examples written below :                     6 -> 1, 2, 3 and 6