The values of x and y are 99 and 343
<h3>The HCF</h3>
The HCF of numbers is the highest common factors of the numbers
<h3>The LCM</h3>
The LCM of numbers is the lowest common multiple of the numbers
The HCF and the LCM are given as:
![HCF = 21](https://tex.z-dn.net/?f=HCF%20%3D%2021)
![LCM = 1617](https://tex.z-dn.net/?f=LCM%20%3D%201617)
Multiply the HCF and the LCM
![HCF \times LCM = 21 \times 1617](https://tex.z-dn.net/?f=HCF%20%5Ctimes%20LCM%20%3D%2021%20%5Ctimes%201617)
![HCF \times LCM = 33957](https://tex.z-dn.net/?f=HCF%20%5Ctimes%20LCM%20%3D%2033957)
The product of the numbers x and y equals the product of the HCF and the LCM.
So, we have:
![x \times y = 33957](https://tex.z-dn.net/?f=x%20%5Ctimes%20y%20%3D%2033957)
<h3>Prime Factors</h3>
Express 33957 as a prime factor
![x \times y = 3^2 \times 7^3 \times 11](https://tex.z-dn.net/?f=x%20%5Ctimes%20y%20%3D%203%5E2%20%5Ctimes%207%5E3%20%5Ctimes%2011)
Rewrite the equation as
![x \times y = 99 \times 7^3](https://tex.z-dn.net/?f=x%20%5Ctimes%20y%20%3D%2099%20%5Ctimes%207%5E3)
![x \times y = 99 \times 343](https://tex.z-dn.net/?f=x%20%5Ctimes%20y%20%3D%2099%20%5Ctimes%20343)
By comparison:
![x = 99](https://tex.z-dn.net/?f=x%20%3D%2099)
![y= 343](https://tex.z-dn.net/?f=y%3D%20343)
Hence, the values of x and y are 99 and 343
Read more about HCF and LCM at:
brainly.com/question/420337