Odd Number :
Any integer that cannot be divided exactly by 2 is an odd number.
Even Number :
Any integer that can be divided exactly by 2 is an even number. The last digit is 0, 2, 4, 6 or 8
Example 1 :
The sum of three even numbers
Solution :
Let us take any 3 even numbers.
For example,
If a = 2, b = 4 and c = 6
The sum of three even numbers = 2+4+6
= 12
12 is even number.
So, sum of three even numbers is even.
Example 2 :
The sum of three odd numbers
Solution :
Let us take any 3 odd numbers.
For example,
If a = 1, b = 3 and c = 7
The sum of three odd numbers = 1+3+7
= 11
11 is odd number.
So, sum of three odd numbers is odd.
Example 3 :
The product of an even and two odd numbers
Solution :
Let us take an even number and two odd numbers.
For example,
If even number is 4, then odd numbers are 3 and 7.
product = 4 × (3 × 7)
= 4 × 21
= 84
84 is even number.
So, product of even and two odd numbers is even.
Example 4 :
The sum of four consecutive odd numbers.
Solution :
If x be the first odd number, then four consecutive odd integers are
x, x + 2, x + 4, x + 6.
Sum of four consecutive odd numbers
= x+(x+2)+(x+4)+(x+6)
= 4x+12
= 4(x+3)
x is odd 3 is also odd, sum of odd and odd will given even number and product of even and even is even.
Example 5 :
(even)3 means ‘an even number is raised to the power 3’. Which of these are odd and which are even ?
(i) (even)2 (ii) (odd)2 (iii) (even)3 (iv) (odd)3
(v) (even)4 (vi) (odd)4
Solution :
(i) (even)2
(even)2 = even × even
= even
(ii) (odd)2
(odd)2 = odd × odd
= odd
(iii) (even)3
(even)3 = even × even × even
= even × even
= even
(iv) (odd)3
(odd)3 = odd × odd × odd
= odd × odd
= odd
(v) (even)4
(even)4 = even × even × even × even
= even × even
= even
(vi) (odd)4
(odd)4 = odd × odd × odd × odd
= odd × odd
= odd
Example 6 :
What is the smallest positive whole number which when increased by 1, is divisible by 3, 4 and 5 ?
Solution :
By finding the least common multiple of 3, 4 and 5, we get 60.
60 is exactly divisible by 3, 4 and 5.
So, the required number is 59.
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