Question

if two positive integers A and B are written as a is equal to X^3 Y^ 2 and b is equal to X×Y^3 where x and y are prime numbers then find the HCF a and b​

Answer 1

Step-by-step explanation:

If two positive integers a and b are written as a = x3y2 and b = xy3, wfiere x, y are prime numbers, then HCF (a, b) is

(a) xy                         

(b) xy2                      

(c)x3y3                          

(d) xy²

According to question find the HCF of (a,b).

(b) Given that, a =x3y2 = x × x × x × y × y

and b = xy3 = x × y × y × y

∴ HCF of a and b = HCF (x3y2,xy3) = x × y × y = xy2 

[Since, HCF is the product of the smallest power of each common prime factor involved in the number