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Even, Odd, Prime, Composite Numbers

 

It is tough to imagine life without numbers. Numbers have such an impact on our everyday lives that everything we do is based on them. Phone numbers, time, money, dates, years, and so on. Natural numbers, whole numbers, integers, odd & even numbers, prime numbers, rational numbers, composite numbers are some examples of different types of numbers. Two different types of numbers are discussed here - odd and even, as well as prime and composite numbers.

Mathematical Even and Odd Numbers

Integers are integers without a fractional element, and they can be positive, negative, or zero. For example - ..., -3, -2, -1, 0, 1, 2, 3,....

Even Numbers

Even numbers are integers that are divisible by two. In other words, integers with unit places of 0, 2, 4, 6, and 8 are divisible by two and are even. When even integers are divided by two, there is no residual (i.e. the remainder is 0).

Odd numbers 

Odd numbers, in contrast to even numbers, are integers that are not divisible by two. At their unit place, they have 1, 3, 5, 7, and 9. When you divide an odd number by two, you get 1 as a remainder.

Even numbers have the potential to be positive or negative. Negative numbers are referred to as negative even integers, and positive numbers are referred to as positive even integers. The same principle applies to odd numbers as well.

Odd and Even Numbers in a General Representation

Every even number is represented as (2n), but every odd number is written as (2n-1) or (2n + 1), where n is a natural integer. In the case of integers, 2k and 2k + 1 or 2k – 1 can be used, respectively.

Prime Numbers

A prime number is a natural number divisible by precisely two numbers, namely 1 and the number itself. In simple terms, a prime number can only be divided by 1 and itself. Except for the number 2, every prime number is an odd number.

Composite Numbers 

A composite number is any non-prime number. Natural numbers with more than two components are known as composite numbers. These integers are also divisible by other numbers.

Here are some interesting facts about prime numbers and composite numbers:

  • The number one is neither prime nor composite.
  • Two is the only even number that is a prime. It's the smallest prime number.
  • All prime numbers, except for 2, are odd numbers.
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