# Even Numbers

When divided by 2, those number does not leave the remainder is called an Even Number. Examples of Even numbers include 2, 4, 6, and many more. We can also say that these numbers are easily divisible by 2. Those numbers whose last digit ends with 0, 2, 4, 6, or 8 will always be even numbers. How to Recognize that the Given Number is Odd or Even?

The simple way to determine whether the number is odd or even is that check its one's place (Unit). The particular will give you an idea of the number. For the even number, the one's place should be 0, 2, 4, 6, 8, and for the odd number, the one's place should be 1, 3, 5, 7, 9. It is the most basic method to determine whether the number is odd or even.

### Properties of the Even Number • Addition of even and odd numbers. The outcome will remain odd.
For example; 2 + 3 = 5
• In addition to the even number with the even number, the outcome will remain even.
For example: 6 + 4 = 10
• The outcome will be even by adding an odd number with another odd number.
For example, 3 + 3 = 6
• The outcome will be odd when even is subtracted from the odd or vice versa.
For example, 6 - 5 = 1
: 5 - 4 = 1
• The outcome will always be even when an even number is subtracted from an even number.
For example: 16 - 6 = 10
• The outcome will always be an even when the odd number is subtracted from odd
For example: 13 - 11 = 2

### Properties of Multiplication

• The outcome will be an even number when an even number is multiplied by an even number.
For example: 2 x 4 = 8 and 12 x 2 = 24
• The outcome will be an even number when an even number is multiplied by an odd number.
For example: 4 x 5 = 20 and 11 x 4 = 44
• The outcome will be an odd number when the odd number is multiplied by an odd number
For example: 9 x 11 = 99 and 13 x 5 = 65

### Odd Numbers

• Numbers that can be written in the form of 2n +1, and here n denotes the natural number.
• Numbers cannot be divided into two equal half parts.
• Those number, when divided by 2, leaves a remainder
• Examples of Odd numbers include: 1, 3, 5, 7, 9

### Even Numbers

• Numbers that can be written in the form of 2n is called even number, where n is a natural number.
• These numbers can be divided into two equal parts.
• When an even number is divided by 2, it leaves no remainder.
• Examples of even numbers include; 2, 4, 6, 8, 10

### Solved Problems

Question: Determine the four consecutive even numbers between 11 to 19.

Answer: Numbers between 11 to 19 are 11, 12, 13, 14, 15, 16, 17, 18, and 19.

So It is clear from above the number series that the four consecutive even numbers would be 12, 14, 16, and 18.

Question: Write the formula for the sum of the first n-even number series.

Answer: The formula for the determination of the sum of the first n-even number of series: n (n + 1)

Question: What is the smallest positive even number?

Answer: The smallest positive even number is 2.

Question: Is 293093490 an even number?

Answer: Yes, it is an even number because it's one place ending with zero.

Question: Determine the sum of all even numbers from 1 to 200.

Answer: Total number that lies between 1 to 200 = 100

We have the formula S = n (n + 1). The formula will help with calculating the sum

Here n = 100

Therefore, putting the values of n into the formula n (n + 1)

S = 100 (100 + 1)

S = 10000 x 101

S= 10100

The total sum = 10100

Question: What is the difference between two odd numbers?

Answer: The difference between the two odd numbers always remains even. 7 and 9 is the odd number. After subtracting seven from 9, the outcome will be 2.

9 - 7 = 2

Question: What is the difference between two even numbers?

Ans: The difference between two even numbers gives an even number. 12 and 10 is the even number. If ten is subtracted from 12, the outcome will be 2.

Question: Are there any divisibility criteria for an Even number?

Answer: Yes, all even number is divisible by 2, meaning they do not leave any remainder. The number can also be divided into two equal parts.

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