Question

What is co-prime? Give examples of five pairs of co-primes. Are co-prime are always positive? If not, illustrate your answer by example.

Answer 1

Hint: The question is simply based on the concept of co primes. For that we should know what co-prime numbers mean. It is the numbers with only 1 as a common factor. Now we can answer the sub questions of the question above.

Complete step-by-step solution:
We know that prime numbers are those numbers that have 1 and the number itself as their factor.
But this is not co prime.
Co prime numbers are those that have only 1 as their common factor but the number or that pair or group need not to be prime numbers only.
Now we will take some examples of coprime numbers.
1). 4 ,15
Factors of 4 are 1,2,4
Factors of 15 are 1,3,5,15
These two numbers have only 1 as a common factor.
2). 18, 43
Factors of 18 are 1,2,3,6,9,18
Factors of 43 are 1,43
These two numbers have only 1 as a common factor.
3). 2, 9
Factors of 2 are 1,2
Factors of 9 are 1,3,9
These two numbers have only 1 as a common factor.
4). 33, 10
Factors of 33 are 1,3,11,33
Factors of 10 are 1,2,5,10
These two numbers have only 1 as a common factor.
5). 1,3
Factors of 1 are 1
Factors of 3 are 1,3
These two numbers have only 1 as a common factor.
Now as we can observe above, in all the five examples we deal with positive numbers only.
Talking about negative numbers we can say that we have never observed negative numbers for co prime numbers.
Suppose -23 and -22 are two numbers. They can be said to be coprime since both have only 1 as a common factor. But the thing is we have never defined negative numbers for co prime numbers.

Note: Note that co prime numbers are also known as relatively prime numbers.
Note that twin prime numbers are only the prime numbers that differ by 2. So always remember the difference between twin prime and coprime basically.