# Coprime Numbers

Go back to  'Numbers'

 1 What are Coprime Numbers? 2 Coprime Numbers Calculator 3 Tips and Tricks to Find Coprime Pairs 4 Coprime Numbers From 1 to 100 5 Properties of Coprime Numbers 6 Important Notes of Coprime Numbers 7 Solved Examples of Coprime Numbers 8 Practice Questions of Coprime Numbers 9 Maths Olympiad Sample Papers 10 Frequently Asked Questions (FAQs)

We at Cuemath believe that Math is a life skill. Our Math Experts focus on the “Why” behind the “What.” Students can explore from a huge range of interactive worksheets, visuals, simulations, practice tests, and more to understand a concept in depth.

Book a FREE trial class today! and experience Cuemath’s LIVE Online Class with your child.

## What are Coprime Numbers?

If the only 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.

### How to Find Coprime Numbers?

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

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

Example 1:

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 HCF $$(6, 10) = 2$$.

Thus, $$(6,10)$$ is NOT a coprime pair. CLUEless in Math? Check out how CUEMATH Teachers will explain Coprime Numbers to your kid using interactive simulations & worksheets so they never have to memorise anything in Math again!

Explore Cuemath Live, Interactive & Personalised Online Classes to make your kid a Math Expert. Book a FREE trial class today!

Example 2:

Let us consider two numbers $$5$$ and $$9$$.

The factors of $$5$$ are $$1$$ and $$5$$.

The factors of $$9$$ are $$1,3$$ and $$9$$.

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

HCF of $$(5,9)=1$$

Thus, $$(5, 9)$$ is a coprime pair. Coprime numbers are also referred to as relatively prime or mutually prime numbers.

### Coprime Number Examples

From Example 2, we know that $$5$$ and $$9$$ are coprime numbers.

Some other coprime number examples (coprime pairs) are:

1. $$2$$ and $$3$$
2. $$15$$ and $$17$$
3. $$9$$ and $$10$$

### Coprimes Factors

The only common factor of coprime numbers is $$1$$

Thus, coprimes factor is $$1$$

## Coprime Numbers Calculator

Here is the Coprime Numbers Calculator.

Here you can enter two numbers, see their factors, their HCF and also you can see whether they are coprime or not. Tips and Tricks
1. Any two prime numbers are coprime.
2. Any two consecutive numbers are coprime.
3. $$1$$ forms a coprime pair with any other number.
4. A prime number is coprime with any other number that is not its multiple.
5. Two even numbers are NEVER coprime.

## Coprime Numbers from 1 to 100

There are many coprime pairs from $$1$$ to $$100$$.

Using the above definition and "Tips and Tricks to Find Coprime Pairs," some coprime numbers from $$1$$ to $$100$$ are:

• $$13, 17$$
• $$15, 16$$
• $$1, 10$$
• $$7, 15$$

Since there are multiple such combinations, it is difficult to determine the coprime numbers list from $$1$$ to $$100$$.

Help your child score higher with Cuemath’s proprietary FREE Diagnostic Test. Get access to detailed reports, customised learning plans and a FREE counselling session. Attempt the test now.

## 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, HCF $$(5, 9)=1$$.

• 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 $$5 \times 9=45$$.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus