Odd numbers room the numbers the cannot be divided by 2 evenly. It cannot be split into two different integers evenly. If we division an weird number by 2, climate it will leave a remainder. The examples of strange numbers room 1, 3, 5, 7, etc. Odd number are simply the opposite principle of even numbers.

The most simple way to remember an odd number is ‘it is not a lot of of 2’. Here, all the principles related to it prefer definition, examples, properties, types, etc. Space covered. The an essential concepts that room covered here include the following.

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Table the ContentTypes

What space Odd Numbers?

Odd numbers are characterized as any type of number which cannot be separated by two. In other words, a number in kind of 2k+1, where k ∈ Z (i.e. Integers) are dubbed odd numbers. It need to be provided that number or sets of integers on a number line have the right to either be odd or even.

Odd Numbers and Even Numbers

The number that are not weird are also numbers, which room divisible by 2. Weird numbers can not be divided into two components equally but even numbers can be separated equally. Because that example, 4 can be divided and paired right into two components as 2-2, yet 3 can not be divided and paired.

Learn more: Even and Odd Numbers

Facts to Remember

A few more vital points come remember:

An strange number is one integer which is not a multiple of 2If this numbers are separated by 2, then there will certainly remainder leftIn the number line, 1 is the an initial positive odd number

Odd Numbers graph (1 to 100)

This chart consists of odd numbers from 1 come 100. Girlfriend can additionally practice creating the odd number from 1 come 1000 in your notebook.

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List of strange Numbers

There are 25 odd numbers from 1 come 50 if there are 50 in in between 1 and 100. In instance of numbers from 1 come 1000, there room 500 odd numbers and also 500 even numbers.

Number RangeNo. Of odd Numbers
1 to 5025
1 come 10050
1 to 200100
1 come 300150
1 to 500250
1 to 1000500
1 come 100005000

Odd numbers from 101 to 200

101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199.

Odd number from 201 to 300

201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271, 273, 275, 277, 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299.

Odd number from 301 to 400

301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399.

Odd numbers from 401 to 500

401, 403, 405, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 435, 437, 439, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 465, 467, 469, 471, 473, 475, 477, 479, 481, 483, 485, 487, 489, 491, 493, 495, 497, 499.

Properties of strange Numbers

There are 4 main nature of odd number are pertained to their addition, subtraction, multiplication, and division. Every of these properties is discussed in the complying with points in a detailed way.

Adding 2 Odd Numbers

Any strange number added to another odd number constantly gives an even number. This declare is additionally proved below.

Odd + strange = Even

Proof:

Let 2 odd numbers be a and b.

These numbers can be written in the type where

a = 2k1 + 1

and b = 2k2 + 1 whereby k1, k2 ∈ Z

Adding a + b us have,

(2k1 + 1) + (2k2 + 1) = 2k1 + 2k2 + 2 = 2(k1 + k2 + 1) i m sorry is for sure divisible by 2.

Subtracting 2 Odd Numbers

When one odd number is subtracted from an odd number, the resultant number will constantly be an even number. This is comparable to including two strange numbers where it was showed that the result was always an even number.

Odd – strange = Even

Multiplication of 2 Odd Numbers

If an odd number is multiplied by an additional odd number, the resulting number will constantly be an odd number. A proof of this is additionally given below.

Odd × weird = Odd

Let 2 odd number it is in a and b. These numbers deserve to be composed in the kind where

a = 2k1 + 1 and b = 2k2 + 1 wherein k1 , k2 ∈ Z

Now, a × b = (2k1 + 1)(2k2 + 1)

So, a × b = 4k1 k2 + 2k1 + 2k2 + 1

The over equation deserve to be re-written as:

a × b = 2(2k1 k2 + k1 + k2) + 1 = 2(x) + 1

Thus, the multiplication of two odd number results is one odd number.

Division of 2 Odd Numbers

Division of two odd numbers constantly results in strange number if and only if the denominator is a variable of the numerator, or else the number an outcome in decimal allude number.

Odd ⁄ weird = Odd

If we summarise the nature of odd number , us have:

OperationResult
ODD + ODDEVEN
ODD – ODDEVEN
ODD x ODDODD
ODD / ODD

*denominator is a variable of the numerator

ODD

Types of odd Numbers

There are mostly two varieties of weird numbers:

Consecutive weird numbersComposite odd numbers

Consecutive odd Numbers

If ‘a’ is one odd number, then ‘a’ and ‘a + 2’ are called consecutive odd numbers. A couple of examples of continuous odd numbers can be

15 and also 1729 and 313 and 519 and 21 etc.

Even for an unfavorable odd numbers, continuous ones will be:

-5 and -3-13 and also -11, etc.

Composite weird Number

A composite strange number is a confident odd integer that is formed by multiplying two smaller positive integers or multiplying the number v one. The composite weird numbers as much as 100 are: 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, 99.

Solved instances on odd Numbers

Example 1: Find the sum of the smallest and also the biggest 3 number odd number and additionally prove the it is divisible by 2.

Solution:

Smallest 3 number odd number = 101

Largest 3 number odd number = 999

Sum that both the numbers = 101 + 999 = 1100

The number 1100 is divisible by 2 (as every the divisibility ascendancy of 2).

This proves that the number is even.

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Example 2: Are the adhering to numbers strange or even?

2515 + 1332 – 37

Solution:

25 is no divisible by 2, therefore odd number.15 + 13 = 28, divisible by 2, no an weird number32 – 37 = -5, is an odd number

Example 3: fill in the blanks with suitable odd numbers:__,2,__,4,__,6,__,8,__,10,__,1222,__,24,__,26,__,28,__,30100,__,102,__,104,__,106,__,108

Solution:1,2,3,4,5,6,7,8,9,10,11,1222,23,24,25,26,27,28,29,30100,101,102,103,104,105,106,107,108

Example 4: How many odd numbers space there between 1 to 100?

Solution: There are 50 weird numbers and also 50 even numbers between 1 come 100.Number that odd numbers = 100/2 = 50

Odd number Worksheet

Is 7 also or strange number?How perform you determine if a number is weird or even?Mention every the odd number which are higher than 60 and smaller 보다 120.List every the odd numbers which are better than -4 and also smaller 보다 20.Is zero an odd number? Why?

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