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Prime Number: Any integer greater than 1 which is divisible only by 1 and itself is a prime number. 2,3,5,7 are prime numbers but 9,15,27 are not primes since these are divisible by 3. remember 0 &1 are not primes.So, how do we determine whether a number is prime or not ?One method is to divide it by all primes less than or equal to the square root of that number. If any of the divisions result in an integer, then the original number is not a prime.
For Example: Let us try to find out if 167 is prime or not.
√167=12.92...............
So, we will attempt to divide 167 by 2,3,5,7,11. 167/2=83.5; 167/5=33.4; 167/7=23.8;167/11=15.18. Since 167 is divisible by none of 2,3,5,7,11 it is a prime.
Odd & Even integers: If an integer is divisible by 2, it is called an even integer, otherwise it is odd.
Even integers: 0,2,14,-4,72,-356,....etc.
Odd integers: 1,3,13,17,-5,-31,...etc.
General representation of odd & even integer: Any even integer can be written as '2n' where 'n' is any integer. So 4=2×2, 56=2×28, 2×3=6
Again any odd integer can be written as 2n+1, where n is any integer.
If n= 3, 2×3+1=7 (odd number)
n=6, 2×6+1=13 (odd number)
n=-2, 2×(-2)+1= -3 (odd number)
So, is odd + even = odd or even?
Is odd × even = odd or even?
Is even × even = odd or even?
Is odd × odd = odd or even?
3 + 2 = 5, odd + even = odd
3 × 2 = 6, odd × even = even
2 + 2 = 4, even + even = even
2 × 2 = 4, even ×even = even
3 × 3 + 9, odd × odd = odd
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