Introducing the topic
Mathematics includes various classifications of numbers as per the properties and similarities. Beginning with the even number and odd number is the basic classification of the whole numbers.
This article deals with a clear understanding of the interesting facts about one of the important types of such numbers, i.e., even numbers. The numbers that can be easily paired up on splitting into the lowest terms are called Even numbers. These are also the multiples of two or in easy words, any number divisible by two and completely satisfying the divisibility of 2 is even. The smallest and only even prime number is taken to be 2.
Hence, the numbers like 2,4,6,8,10,12…102,104…198,200…568,570,…& so on are all even.
Even numbers can’t be understood till the detailing isn’t linked with odd numbers. Odd numbers can be conveniently said to be the antonym for even numbers, i.e., odd numbers are those that cannot be divided by 2 or leave 1 as remainder on being divided by two.
Effect of mathematical operations on even numbers
While performing basic mathematical operations over even numbers certain basics should be kept in mind. Those are listed below:
- Whenever two even numbers are added, the result is even.
- On adding an even to odd the result obtained is odd.
- Adding two odd numbers result in an even number.
- When two even numbers are subtracted the result is even.
- If an odd number is subtracted from any even number the result is odd.
- Subtracting two odd numbers results in an even number.
- The multiplicative property defines that the product of two even numbers is always even.
- When the multiplier is even and multiplicand is odd or vice-versa then the product obtained is even.
These properties also are the facts for the respective mathematical operations, namely, addition, subtraction, multiplication and division. The divisibility rules and similar properties of multiplication and division also play an important role in differentiating between odd numbers and even numbers. The above-listed properties can be verified by performing basic mathematical operations on a different combination of numbers. The basic mathematical operations follow the idea of rules like BODMAS, PEMDAS, BEDMAS etc.
The prime number that is even too
The only even prime number is 2. This is so due to the basic property of even numbers that says that a number is even only when it satisfies the divisibility rule for two and all even numbers have factors other than 2 and 1.
Properties related to odd numbers
Likewise, the odd number also have a set of defined and verified properties that have a versatile application.
- If two odd numbers are added together, their sum will result to be even.
- On subtracting two odds to the difference obtained is again even.
- When it comes to multiplication two odd numbers result in an odd product.
- Lastly, the division of two odd numbers gives an odd quotient.
To be noted, if the odd/ even number is n then the consecutive numbers can be n+2, n+4, n+6, … so on. Whole/ natural/ integer is the category of odd and even numbers.
Fractions and decimals aren’t subject to the classification of odd and even.
On the division of any number by another, the divisor must divide the dividend completely to identify it as even or odd.
Cuemath describes the concept efficiently and the related topics plus the respective number charts are given on the application to ensure a detailed description of the same. The related charts as even and odd numbers ranging from 1-100, the types of prime and composite numbers in relation to the topic, solved and unsolved problems related to the topic are given under the specific head.