The co-prime numbers will be the set of numbers or integers which have only one as their common factor and this will be the highest common factor in this particular case. The coprime number is also referred to as relatively prime or mutually prime numbers and further, it is very much important for the people to be clear about the concept of numbers that there should be two numbers to form co-primes.
How to Find Out the Co-Prime Numbers?
For this, the people need to consider a set of numbers that have no positive integer that can divide both other than one. Then the pair of numbers will be considered as co-prime.
Example 1: The set of numbers here is 21 and 22
The factors in this case of 21 will be 1, 3, 7, 21
The factors of number 22 will be one, two, 11, and 22.
Here 21 and 22 will have only one common factor which is the highest common factor which is the main reason that they will be co-prime.
Example 2: In this particular area numbers will be 21 and 27.
The factors of number 21 will be 7, 3, 1 and 21
The factors of number 27 will be 1, 3, 9 and 27
Here, there will have to common factors which will be one and three and the highest common factor will be three which is the main reason that they will not be co-prime.
Following are the most important properties of the co-prime numbers:
- One will be the co-prime with every number
- Any two prime number will be co-prime to each other because two of the prime numbers will have only one and number itself as the common factor which is the main reason that they are co-prime. For example, two and three will be co-prime numbers with each other.
- Any two successive numbers or integers will always be co-prime for example consecutive numbers like two and three, three and four, five and six, and so on because they will have only one has the highest common factor in both of them.
- The sum of any two co-prime numbers will always be co-prime with their product, for example, two and three are co-prime and the sum is five and the product is six. So, five and six are co-prime to each other.
- Two even numbers can never become co-prime pairs because they will always have the common factor as two.
- If two numbers of the unit digit 0 as well as five then also they will not be co-prime to each other for example 10 and 15 because they will be divisible by five and five will become the highest common factor in this particular case.
Some of the pairs of co-prime numbers from one-hundred are mentioned as follows:
13 and 14, 46 and 67, 75 and 41, 28 and 57, two and 87, one and 99, and several other kinds of pairs
The prime numbers will be defined as the number which has no other factor than one and number itself and on the other hand co-primes will be considered in pairs and two numbers will only be co-prime if they have no other common factors and one. Finding out the co-primes of any of the numbers will be based upon finding the factors of the number first and then choosing the number as well as finding the factors of that particular number. The process is very easy. Hence, to be aware of this particular concept and to learn the things perfectly associated with the prime numbers and co-prime numbers it is very much important for the students to enrol themselves on Cuemath so that they can fetch good marks in the examination very easily.
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