UNDERSTANDING CO-PRIME NUMBERS

WHAT ARE CO-PRIME NUMBERS?

Any two numbers can be co-prime numbers when they only have one factor in common which is the number 1. We need at least two numbers to form a set of these co-prime numbers. Consider the numbers 5 and 7. They have only one factor in common which is the number 1 so these are co-prime numbers. 

CO-PRIME AND PRIME NUMBERS

Co-prime numbers are different from prime numbers. While prime numbers have only two factors which are the 1 and the number itself, it is not the case with co-prime numbers. Co-prime numbers are a set of numbers that only have 1 as their common factor.

HOW TO FIND CO-PRIME NUMBERS?

The easiest way to find a co-prime number is to find out the HCF or highest common factor. The highest common factor is the greatest possible number which divides both the numbers exactly. So, if the highest common factor between two or more numbers is 1 then they are co-prime numbers.

PROPERTIES OF CO-PRIME NUMBERS

1. Any two prime numbers are co-primes. {for example: (5,7), (2, 11)}.
2. The set of co-prime numbers can have one prime and one composite number {for example: (4,7), (2,9)}
3. The set can also be made with both composite numbers (numbers that are not prime are called composite numbers) {for example: (4, 9), (8, 11)}
4. The highest common factor of co-prime numbers is always 1. 
5. The number 1 itself is a co-prime with every other number.
6. The lowest common factor of any two co-prime numbers is simply their product. For example, the LCM of 5 and 7 is (5 x 7) = 35.
7. Any two consecutive numbers are co-primes. For example, (1,2), (2,3), (3,4).
8. Any two even numbers can never be co-primes because all even numbers have two or more common factors. For example, (12, 14).

 Numbers that divide 12 completely (factors) are 1, 2, 3, 4, 6, 12. 

Numbers that divide 14 completely (factors) are 1, 2, 7, 14. The common factors for 12 and 14 are 1 and 2. Therefore, they are not co-primes.

CO-PRIME NUMBERS FROM 1 to 100

Co-prime numbers from 1 to 100 include all the consecutive numbers which are (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10, 11), (11, 12), (12, 13) and so on.

It also includes the set of all prime numbers which are (5,7), (7,11), (13,17), (5,31), (61,11) , (53,11) along with all possible combinations of prime numbers from 1 to 100 ( prime numbers: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)

Two composite numbers can also form co-prime numbers such as (4,9), (8,15), (16,21) and so on. 

A pair of prime and composite numbers that can be co-primes are (3,10), (8, 13), (7, 15), (11, 20) and so on.   

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