If two positive integers a and b are written as a = x³y² and b = xy³ ; x, y are prime numbers, then HCF (a, b) is
a. xy
b. xy²
c. x³y³
d. x²y²

Solution:

It is given that,

a = x³y² = x × x × x × y × y

b = xy³ = x × y × y × y

The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.

As HCF is the product of the smallest power of each common prime factor involved in the numbers.

HCF of a and b = HCF (x³y², xy³)

= x × y × y

= xy²

Therefore,HCF (a, b) is xy²

✦ Try This: Let us find the HCF and LCM of 6 and 8 to understand their relationship

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.1 Problem 6

If two positive integers a and b are written as a = x³y² and b = xy³ ; x, y are prime numbers, then (a, b) is a. xy, b. xy², c. x³y³, d. x²y²

Summary:

If two positive integers a and b are written as a = x³y² and b = xy³ ; x, y are prime numbers, then HCF (a, b) is xy²

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