Question

Find whether the numbers are relatively prime or not : $224,243$

Short answer

It is a relatively prime number.

Step-by-step solution

Step -1 - Apply the concept of   GCF and relatively Prime

In this, simply use the concept of finding the GCF by doing the factors of the number and find the factor which is common and greatest from them and also know the concept of relatively prime that means those whose have a only factor $1$ not other than any other.

Step -2 – Find the common factors

Here, the numbers are $224,243$.

First finding the factors of numbers.

The factor of $224$is localid="1649289840553" $224=2\times 2\times 2\times 2\times 2\times 7$

The factor of $243$ is $243=3\times 3\times 3\times 3\times 3$

Step -3 – Finding the GCF and know whether it is relatively prime or not

Now, the common factor among the numbers are $1$.

So, the greatest common factor is $1$.

Since, the two numbers have HCF of $1$, therefore they are relatively prime.