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What are Co-Prime numbers?

In this mini-lesson, we will explore the world of coprime numbers by finding the answers

to the questions like how to find coprimes, how the coprimes are determined and how to

find the HCF of 2 numbers while discovering the interesting facts around them.

Two numbers are co-prime if their common factor is only 1.

Doesn't it sound interesting! Let's explore further.

Lesson Plan

1. What are Coprime Numbers?

2. Tips and Tricks

3. Properties of Coprime Numbers

4. Important Notes

5. Solved Examples on Coprime Numbers

6. Practice Questions on Coprime Numbers

7. Summary

8. Frequently Asked Questions

What are Coprime Numbers?

If the only common factor of two numbers a and b is 1, then a and b are coprime

numbers.

In this case, (a, b) is said to be a coprime pair.

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How to Find Coprime Numbers?

To find whether any two numbers are coprime, we first find their GCF.

If their GCF is 1 , we can say that they are coprime.

Example 1:

Let us consider two numbers 5 and 9

The factors of 5 are 1 and 8.

The factors of 9 are 1, 3 and 9.

The factor that is common to both 5 and 9 is 1.

GCF of (5, 9) = 1.

Thus, (5, 9) is a coprime pair.

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Example 2:

Let us consider two numbers 6 and 10

The factors of 6 are 1,2,3 and 6

The factors of 10 are 1,2,5 and 10

Factors that are common to both 6 and 10 are 1 and 2

So GCF (6, 10) = 2

Thus, (6,10) is NOT a coprime pair.

Coprime numbers are also referred to as relatively prime or mutually prime numbers.

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Unlock the Mystical World of Coprime Numbers

Is it not fun to learn about the coprime numbers? Would you be interested in the other

lessons around this concept?

Click on a mini lesson to explore further!

Factors

Composite Numbers

Least Common Multiple

Prime Factorization

Prime Number

Perfect Numbers

Properties of Coprime Numbers

Some properties of coprime numbers are:

• The HCF of two coprime numbers is always 1

For example:

5 and 9 are coprime numbers and hence, GCF (5, 9)=1

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• The LCM of two coprime numbers is always their product.

For example:

5 and 9 are coprime numbers.

Hence, LCM (5,9) = 45

• The sum of two coprime numbers is always coprime with their product.

For example:

5 and 9 are coprime numbers.

Here, 5+9=14 is coprime with 5 \times 9=45

Coprime Numbers From 1 to 100

• 2 Prime numbers have only 1 as their common factor. Consider 29 and 31.

29 has 2 prime factors. 1 and 29 only

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31 has 2 prime factors. 1 and 31 only.

29 and 31 are prime numbers. They have only one common factor 1.

Thus they are co-prime.

We can check any two prime numbers and get them as coprime.

For example: 2 and 3, 5 and 7, 11 and 13 and so on.

• Any 2 consecutive numbers have 1 as their common factor.

Consider a few pairs of such numbers. Let us try with 14 and 15.

Numbers 14 15

Factors 1,2,7,14 1,3,5,15

Common Factor 1

There are multiple such combinations as 1 is the only common factor.

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Solved Examples

Show that 161 and 192 are coprime numbers.

Solution

We will find the HCF of the given numbers 161 and 192 using the division method.

Example 1

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The HCF of 161 and 192 is 1.

Thus, they are coprime numbers.

∴ 161 and 192 are coprime.

If 59 and 97 are coprime, what would be their HCF?

Solution

It is given that 59 and 97 are coprime.

They cannot have any common factor other than 1.

Hence, their HCF is 1.

∴ HCF of (59, 97)=1

If 13 and 5 are coprime numbers, what is their LCM?

Solution

It is given that 13 and 5 are coprime numbers.

Hence, their LCM is equal to their product, 13 \times 5 = 65.

∴ LCM (13,5)=65

Example 2

Example 3

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Practice Questions

Here are a few activities for you to practice.

Q.1 a) Write the common factor of 13 and 17?

____________________

Q. 1 b) Do 13 and 17 form a co-prime pair?

• Yes

• No

Q.2 a) How many factors do 26 and 33 have in common?

• No common factors

• Only 1 common factor

• Only 2 common factors

• More than 2 common factors

Q.2 b) Do 26 and 33 form a co-prime pair?

• Yes

• No

Q.3) Two numbers are said to be co-prime if they share no common factors other than 1.

The common factor of these numbers is always 1.

Both the pairs—(18,35) and (15,17) —are co-prime. So, what will be the HCF of any two

co-prime numbers?

____________________

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Q.4 a) Write the common factor obtained for 19 and 23.

____________________

Q.4 b) Do 19 and 23 form a co-prime pair?

• Yes

• No

Q.5 a) Write the common factor obtained for 27 and 34.

____________________

Q.5 b) Do 27 and 34 form a co-prime pair?

• Yes

• No

Let's Summarize

The mini-lesson targeted in the fascinating concept of coprime numbers. The math journey

around co-prime numbers starts with what a student already knows, and goes on to

creatively crafting a fresh concept in the young minds. Done in a way that not only it is

relatable and easy to grasp, but also will stay with them forever. Here lies the magic with

Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite

readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers

explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the

logical thinking and smart learning approach that we at Cuemath believe in.

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Frequently Asked Questions (FAQs)

1. What are coprime numbers?

If the only factor of two numbers a and b is 1, then a and b are coprime numbers. It is very

difficult to determine the coprime numbers list.

2. What is the difference between prime and coprime numbers?

A prime number is a number that is greater than 1 which has exactly two factors 1 and

itself. Coprime numbers are numbers whose HCF (Highest Common Factor) is 1.

3. How to find the co-prime of a number?

The HCF of two co-prime numbers is 1. Thus, to find the co-prime number of a number, it

is sufficient to find a number which is NOT divisible by any of the factors of the given

number.

4. Which numbers are identified as co-prime numbers?

A single number cannot be co-prime. Two numbers are said to be co-prime if their HCF is

1.

5. Are 18 and 35 co-prime numbers?

The factors of 18 are 1,2,3,6,18. The factors of 35 are 1,5,7,35.

18 and 35 have no common factor other than 1. Thus, 18 and 35 are co-prime.

6. Are co-prime numbers always prime numbers?

No, co-prime numbers don't have to be prime numbers.

For example: 18 and 25 are co-prime numbers as their HCF is 1. But 18 and 25 are NOT

prime numbers.

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Cuemath Worksheet

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Worksheet on Co-Prime Numbers

1. Are 2 consecutive numbers coprime?

YES NO

2. 11 and 13 are co-prime numbers. Why?

3. Can two composite numbers be relatively prime?

TRUE FALSE

4. Circle any five co-prime number pair from the following.

1 4 6 5 8 7 10 11 14 15 13 18 20

5. What is the LCM of coprime numbers?

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6. 12 and 35 are coprime numbers, what is their HCF?

7. List 20 coprime number pairs between 1 and 100?

8. Can a prime number and a composite number be a coprime number pair?

YES NO

9. What is the basic difference between coprime numbers and twin prime numbers?

10. Are 13 and 5 coprime numbers? Justify your answer.

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Cuemath Tips and Tricks

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Co-Prime numbers - Tips and Tricks

● All prime numbers are co-prime numbers, their HCF is 1

● Co-prime numbers need not be prime numbers. For example,

(4,9) are not prime numbers but they are coprime as they have

only 1 as a common factor.

● 1 is coprime with any number.

● The sum of any two co-prime numbers will also be coprime

with the product of the same two coprime numbers.

● If a and b are coprime numbers, then a2 and b2 will also be co-

prime numbers.