Numbers in mathematics influence the lives of people from the day they are born. Day one or date of birth to the age that changes every year. You cannot imagine your lives without numbers. Money, time, the mobile numbers of close ones, important dates, numbers play a very important role in everyone’s lives. The subject of mathematics has a vast syllabus full of all kinds of numbers, like even, natural, whole, integers, prime, rational, etc.
The odd numbers are the ones that are not divisible by 2 consistently. A remainder is left behind if we try to divide the odd numbers by 2. The examples of odd numbers are 3,5,1,7 and so on.
Some important points to note are:
- An odd number is known as an integer, that is not divisible by two
- If you try to divide such numbers by two, they leave a remainder
- At the start of the number line, number 1 is the positive first odd number
Odd numbers have four major properties, which are explained as follows:
- Addition: The result that you get when two odd numbers are added together is always an even number.
- Subtraction: In a similar manner. The result that you derive when two odd numbers are subtracted from each other is always an even number.
- Multiplication: The result that you get when you multiply two odd numbers together will always be an odd number.
- Division: Similarly on dividing two odd numbers you always get an odd number as the answer, only if the denominator is a numerator’s factor. Otherwise, the resulting number is generally a decimal point.
Odd numbers are of two kinds:
- Consecutive: Suppose x is an odd number, so the consecutive odd number would be x and x+2, for example
12 and 12+2 = 12 and 14
8 and 8+2 = 8 and 10 etc.
- Composite: This number is formed when you multiply two positive integers that are small or you multiply with one. The example of composite odd numbers is 15, 35, 49, and so on.
Mutually Prime or Co-Prime Numbers
The set of numbers or integers is known as Co-Prime when they have only one as their common factor. Number 1 is the Highest common factor. These numbers are also called mutually prime or relatively prime. The coprime numbers can only be formed if there is a set of two numbers at least.
Let’s have a look at the properties of Mutually Prime numbers
- Number 1 is mutually prime with each and every number.
- All prime number factors are number 1 and the number itself. For example, 2 and 3 are prime numbers. Number 2 has 1, 2 as factors, and number 3 has 1, 3 as factors. The common factor is 1 and hence all prime numbers are co-prime.
- Any two consecutive numbers are co-prime. Take the consecutive numbers like 2, 3 or 5, 6, and so on. Their HCF is 1.
- The total sum of any two co-prime numbers is always co-prime with the product they get.
- Even numbers can never form a pair of coprime numbers, as all of them can be divided by 2.
Prime and co-prime numbers are different from each other. They have a slight difference. A prime number is a single number, that has itself and number 1 as a factor. Whereas co-prime numbers are always calculated in pairs, and they do not have any other common factor than 1.
You cannot master the subject of mathematics without getting all your numbers right. It is really important to understand the differences and logic about all kinds of numbers. Cuemath is definitely the best choice if you want to refer to the notes online. They provide you with the expert advice required. You have a lot of worksheets that you can solve, to improve your skills in calculation. The trick to master any subject in mathematics is to practice as much as you can. You have to do just that.