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If two positive integers a and b are written as a = x3y 2 and b = xy3 , where x, y are prime numbers, then HCF (a, b) is ?

Read more at: https://edurev.in/question/3682600/If-two-positive-integers-a-and-b-are-written-as-a-x3y2-and-b-xy3--where-x--y-are-prime-numbers--then?
Most Upvoted Answer
If two positive integers a and b are written as a = x3y 2 and b = xy3 ...
Solution:


To find the highest common factor (HCF) of two numbers, we need to identify the common factors of both numbers and choose the highest one.

Given that:
a = x^3 * y^2
b = x * y^3

We can find the common factors of a and b by comparing their prime factors.

Prime factorization of a:

The prime factorization of a is given as x^3 * y^2.

Prime factorization of b:

The prime factorization of b is given as x * y^3.

Common factors of a and b:

To find the common factors, we need to compare the prime factors of a and b. The common prime factors are the ones that appear in both factorizations.

The common prime factors of a and b are:
x (appears in both factorizations)
y^2 (appears in the factorization of a)
y^3 (appears in the factorization of b)

HCF (a, b):

The HCF is the product of the common prime factors raised to the lowest power they appear in both factorizations.

HCF (a, b) = x * y^2

Therefore, the highest common factor of a and b is x * y^2.
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