PRIME AND COMPOSITE NUMBERS
EVEN NUMBERS:-
All numbers divisible by ‘2’ are called even numbers 2, 4, 6, 8 ......
ODD NUMBERS:-
Numbers which are not divisible by ‘2’ are called odd numbers 1, 3, 5........
General form of even and odd numbers
1. General form of even number can be written as
General form of odd numbers can be written as
2. \(E = \{ 0,2,4,...........\} \) , \(O = \{ 1,3,5,...........\} \)
Some facts about even and odd numbers
1. The sum or product of any number of even numbers is even
Ex:- 4 + 2 = 6 and \(4 \times 6 = 24\)
2. The difference of two even numbers is even
Ex:- 4-2=2
3. The sum of odd numbers depends on the number of numbers
a) If the number of numbers is odd sum of the numbers is odd
Ex:- 3 + 5 + 9 = 17(odd)
b) If the number of numbers is even the sum is even
Ex:- 3 + 5 + 7 + 9 =24(even)
4. If the product of a certain number of numbers is odd, then none of the numbers is even
\(3 \times 5 \times 7 = 105(odd)\)
i.e the product of any number of odd numbers is odd.
5. If the product of certain number of numbers is even, then atleast one of them is even.
7 x 5 x 10 = 750
6. If \(2n(n \in I)\) is even number, then odd number is \((2n \pm 1)(n \in z)\)i.e., the difference of even and odd number is ‘1’
i.e. 2n- (2n -1) = 2n - 2n +1 =1