What are the Co-Prime Numbers?

Co-Prime Numbers, also called 'Relatively Prime Numbers', are like best friends - they don't have other friends in common except for the number 1.

To be Co-Prime, two numbers must have a Highest Common Factor or HCF of 1, which means they don't have any other factors in common.

For example, let's say we have two numbers, x and y. If the only common factor between x and y is 1, then x and y are Co-Prime Numbers. This means they are special friends who don't have any other friends in common except for the number 1.

Co-Prime Numbers from 1 to 100

Let's look at some examples of Co-Prime Numbers from 1 to 100 :
(3, 8)
(5, 12)
(7, 22)
(11, 26)
(19, 27)
(33, 47)
(44, 63)
(65, 91)etc.

They're like secret agents with a special connection that nobody else knows about except for the number 1.

How to Check if the Given Set of Numbers is CoPrime?

To determine if a set of numbers is CoPrime, we need to find their factors. If they only have 1 as a common factor, then they are CoPrime.

1. 14 and 15

Factors of 14 are 1, 2, 7 and 14.
Factors of 15 are 1, 3, 5 and 15.
The Common factor of 14 and 15 is only 1. So, 14 and 15 are CoPrime Numbers.

2. 7 and 22

Factors of 7 are 1 and 7.
Factors of 22 are 1, 2, 11 and 22.
Common factors of 7 and 22 are only 1. So, 7 and 22 are CoPrime Numbers.

3. 12 and 16

Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 16 are 1, 2, 4, 8 and 16.
Common factors of 12 and 16 are 1, 2 and 4. So, 12 and 16 are not CoPrime Numbers.

Properties of Co-Prime Numbers

Co-Prime Numbers have some interesting properties that make them unique. Here are some of them:

1. 1 is CoPrime with every Number.

2. Every Prime Number is Co-Prime to Each Other

Since every Prime Number has only two factors - 1 and the number itself, any two Prime Numbers will only have 1 as their common factor.

For example, 7 and 17 are both Prime Numbers. The factors of 7 are 1 and 7, while the factors of 17 are 1 and 17. Since the only common factor between them is 1, 7 and 17 are Co-Prime.

3.Any two successive Numbers are always CoPrime:

If we take any two numbers that come one after the other, like 3 and 4, or 7 and 8, or 14 and 15, then the only common factor between them is 1.

4. Sum of any two Co-Prime Numbers is always CoPrime with their product.

For example, 3 and 4 are Co-Prime and have 7 as their sum (3+4) and 12 as the product (3×4). Hence, 7 and 12 are Co-Prime to each other.

Co-Prime Number Examples

1. Check CoPrime Numbers from the Given Set of Numbers

20 and 35
7 and 17
14 and 15

Answer:
a) 20 and 35 are not a CoPrime Number because their Common factors are 1 and 5.
b) 7 and 17 are CoPrime Numbers because they are Prime Numbers.
c) 14 and 15 are CoPrime Numbers because they are two successive Numbers.

2. What is the Difference Between Prime Numbers and CoPrime Numbers?

A Prime Number has only two factors, 1 and itself, while CoPrime Numbers are pairs of numbers that only have 1 as their common factor. This means their highest common factor (HCF) is 1.