If two positive integers a and b are written as a and x3y2 and b = xy3, where x, y are prime numbers, then HCF(a, b) isa)xyb)xy2c)x3y3d)x2y2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

I think Option 'b' is Correct because see-->
a=x^3y^2,
b=xy^3,
or,
a=x.x.x.y.y,
b=x.y.y.y,
HCF(a,b)=xy^2

Answer

Answer

Illustration -- Let us suppose x=3 and y=5.. then HCF of 3^3×5^2 and 3×5^3 will be 3^3×5^3 .... hence answer is x^3×y^3...

Answer

Here, a = x3y2 and b = xy3.
⇒ a = x * x * x * y * y and b = xy * y * y
∴ LCM(a, b) = x * x * x * y * y * y = x3 * y3 = x3y3
LCM = x3y3

Answer

To find the highest common factor (HCF) of two positive integers a and b in the given format, we need to analyze the prime factorization of both numbers.

Prime factorization of a:
a = x^3 * y^2

Prime factorization of b:
b = x * y^3

To find the HCF, we need to determine the common prime factors of a and b, and take their lowest powers.

Finding the common prime factors:
The common prime factors of a and b are x and y.

Determining the lowest powers:
- For the prime factor x, the power in a is 3, and the power in b is 1. So, the lowest power of x is 1.
- For the prime factor y, the power in a is 2, and the power in b is 3. So, the lowest power of y is 2.

Therefore, the HCF(a, b) is given by the product of the common prime factors raised to their lowest powers.

HCF(a, b) = x^1 * y^2 = xy^2

Hence, the correct answer is option C, HCF(a, b) = x^3 * y^3.

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