Question

if two positive integers A and B can be expressed as A=xy3=B=x4y2z;x,y being prime numbers then HCF A,B is​

Answer 1

Answer:

hello there,,,, here is your solution

HCF by using the prime factorization method.

Step1:

Find the prime factorization of each of the number

Step2:

The product of all common prime factor is the HCF

Here,

⇒a=x×x×y×y

⇒b=x×y×y

common Factors are x×y×y

Thus ,

HCF(a,b)=xy

2

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Answer 2

Given : two positive integers A and B can be expressed as

A = xy³

B = x⁴y²z

x , y and z being prime numbers

To Find : HCF (A,B)

Solution:

x , y and z being prime numbers

Hence no common prime factors between x , y and z

HCF Highest common factor is highest power polynomial and largest power numeric coefficient expression which can divide all the expressions.

HCF = product of common factors of least power

A = xy³

B = x⁴y²z

Least power of  x= 1

Least power of y = 2

Least power of z = 0   as A does not have z as factor

Hence HCF (A , B )  = xy²

HCF (A , B )  = xy²

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