Even Numbers 1 to 100: Definition, Examples, and Properties

Even Numbers

Even Numbers Explained: Whole numbers are categorized into even and odd numbers. An even number is any integer that can be divided by 2 without leaving a remainder. Conversely, if a division by 2 results in a remainder, the number is odd. To master identifying even numbers, it is helpful to familiarize yourself with the 2-times table and basic division. Here are some examples:

Let's analyze the following numbers: 4, 19, 54, and 488. 

Using the 2-times table, we can easily identify that 4 is an even number. Conversely, 19 is not an even number because it is not perfectly divisible by 2; dividing 19 by 2 results in 9 with a remainder of 1.

Next, consider the numbers 54 and 488: 

                                         54÷2= 27                488÷2=244

Both 54 and 488 are perfectly divisible by 2, leaving no remainder. Among our examples, only 19 is not an even number. This article will guide you through the clear definitions, properties, and essential rules for identifying even numbers.

Even Number Definition

An even number is defined as any integer that is perfectly divisible by 2, or a number that can be split into two equal groups without any remainder. Below, we provide several examples to help you test if a number is even.

Take 8: Dividing 8 by 2 equals 4 with a remainder of 0. Therefore, 8 is an even number.

Take 12: Dividing 12 by 2 equals 6 with a remainder of 0. Therefore, 12 is an even number.

Take 15: Dividing 15 by 2 leaves a remainder of 1. Therefore, 15 is not an even number; it is an odd number.

Take 21: Checking the divisibility of 21 by 2 leaves a remainder of 1. Thus, 21 is an odd number, not an even number.

As demonstrated, numbers that are not divisible by 2 will always leave a remainder and are classified as odd numbers.

Even numbers can also be expressed as any integer in the form n=2k, where k is an integer. 

How to find Even Numbers easily?

The most efficient method to identify an even number is to look at its last digit:

1. If the last digit of a number ends up with 0, 2, 4, 6, or 8. It is even.
2. If the last digit of a number ends up with 1, 3, 5, 7, or 9. It is odd.

For example:

58 is an even number because its last digit is 8.

366 is an even number because its last digit is 6.

987,654 is an even number because its last digit is 4.

23 is not an even number because its last digit is 3; therefore, 23 is odd.

487 is not an even number because its last digit is 7; therefore, it is an odd number.

Even Numbers 1 to 100

There are exactly 50 even numbers between 1 and 100. The full list is provided below.

List of Even Numbers 1 to 100
2	22	42	62	82
4	24	44	64	84
6	26	46	66	86
8	28	48	68	88
10	30	50	70	90
12	32	52	72	92
14	34	54	74	94
16	36	56	76	96
18	38	58	78	98
20	40	60	80	100

Even Numbers 1 to 200

The list of even numbers between 1 and 200 is as follows:

List of Even Numbers 1 to 200
2	22	42	62	82	102	122	142	162	182
4	24	44	64	84	104	124	144	164	184
6	26	46	66	86	106	126	146	166	186
8	28	48	68	88	108	128	148	168	188
10	30	50	70	90	110	130	150	170	190
12	32	52	72	92	112	132	152	172	192
14	34	54	74	94	114	134	154	174	194
16	36	56	76	96	116	136	156	176	196
18	38	58	78	98	118	138	158	178	198
20	40	60	80	100	120	140	160	180	200

Properties of Even Numbers

1. Addition Properties:

a) Adding two even numbers always results in an even number. 

For example: 8+6=14, 14+82=96, 12+6=18.

b) Adding an even number and an odd number (or vice-versa) always results in an odd number. 

For example: 4+9=13, 11+10=21, 22+3=25.

c) The sum of two odd numbers always results in an even number. 

For example: 7+3=10, 9+9=18, 43+65=108.

2. Subtraction Properties:

a) The difference between two even numbers is always an even number.

For example: 16-4=12, 88-8=80, 442-322=120.

b) The difference between an even number and an odd number (or vice-versa) is always an odd number.

For example: 32-9=23, 19-10=9, 40-7=33.

c) The difference between two odd numbers is always an even number.

For example: 7-3=4, 11-9=2, 47-5=42.

3. Multiplication Properties:

a) The product of two even numbers is always an even number.

For example: 8 x 2=16, 14 x 4=56, 2 x 2=4.

b) The product of an even number and an odd number is always an even number.

For example: 4 x 7=28, 3 x 6=18, 12 x 5=60.

c) The product of two odd numbers is always an odd number. Note that this is technically an property of odd numbers.

For example: 5 x 5=25, 11 x 11=121, 13 x 3=39.

Summary of Properties of Even Numbers

Properties of Addition:
1.	Even + Even	Even
2.	Even + Odd	Odd
3.	Odd + Odd	Even
Properties of Subtraction:
1.	Even - Even	Even
2.	Even - Odd	Odd
3.	Odd - Odd	Even
Properties of Multiplication
1.	Even X Even	Even
2.	Even X Odd	Even
3.	Odd X Odd	Odd

Even Prime Numbers

Did you know a prime number has exactly two factors: 1 and itself? Since even numbers are divisible by 2, they cannot be prime unless the number is 2 itself. Therefore, 2 is the only even prime number, as all other even numbers have at least three factors (1, 2, and the number itself). Learn more about prime numbers here. 

Important Points on Even Numbers:

1. In counting, every alternate number is an even number starting from 2 and an odd number starting from 1.
2. 0 ‘Zero’ is an even number.
3. The smallest even number is 2.
4. The only even prime number is 2.

Even Numbers- Solved Questions

Q1: How do you find the sum of n even numbers?

Answer: The sum of the first n even numbers is calculated using the formula S = n(n+1).

Q2: Calculate the sum of the first ten even numbers.

Answer: The sum is calculated using the formula S = n(n+1).

In this case, we need the sum of the first ten even numbers, so n = 10.

       By substituting n=10 into the formula:

        S=10(10+1)

          =10(11)

          =110. You can also cross-check this solution manually.

The first 10 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.

2+4+6+8+10+12+14+16+18+20 = 110. The sum is verified as 110.

Q3: Identify the even numbers from the set: 633, 524, 873, 448, 87, 222, 65, 14872, 8945, 25648.

Answer: The even numbers from the list are: 524, 448, 222, 14872, and 25648.

Total number of items = 84 (even) + 60 (even) = 144 (even).

Q4: List any eight consecutive even numbers between 50 and 70.

Answer: The even numbers between 50 and 70 are 52, 54, 56, 58, 60, 62, 64, 66, 68, and 70. Eight consecutive even numbers from this range include 52, 54, 56, 58, 60, 62, 64, and 66.

Q5: Kamal buys 84 water bottles, and his brother Satyam brings 60. Is the total count even?

Answer: The number of bottles bought by Kamal is 84, which is even.

The number of bottles brought by Satyam is 60, which is also even. 

The total number of bottles is: 

                                        84 (even) + 60 (even) = 144 (even).

Q6: Find the sum of all even numbers from 1 to 200.

Answer: There are 100 even numbers between 1 and 200. 

Here, n = 100.

Using the formula S = n(n+1), we can calculate the total.

Since n=100: 

S = n(n+1)

S = 100(100+1)

S = 100(101)

S = 10,100.

                                 = 10,100.

The sum of all even numbers from 1 to 200 is 10,100.

Q7: Which statement is correct?

1.  The Product of two even numbers is always an even number.
2.  The Sum of two even numbers is always an odd number.

Answer: Statement 1 is correct.

Statement 1: Even x Even = Even (e.g., 6 x 6 = 36, 8 x 6 = 48).

Statement 2 is often a point of confusion; Even + Even = Even, not odd.

For example: 4+8=12, 10+12=22. The sum is consistently an even number.

Q8: Choose the correct option: The difference between two even numbers is:

a) Always an even number

b) Always an odd number

c) Can be both odd and even

d) None of the above

Answer: Option (a) is correct. Even - Even = Even. For example, 8 - 4 = 4; 18 - 6 = 12.

Q9: Is zero (0) an even number? Justify.

Answer: Yes, zero is an even number. Since 0 divided by 2 equals 0 with no remainder, it satisfies the definition of an even number.

Q10: What is the sum of 4 consecutive even numbers between 20 and 30?

Answer: The four consecutive even numbers between 20 and 30 are:

22, 24, 26, and 28. Their sum is 22 + 24 + 26 + 28 = 100.