Find the HCF of a = x³y² and b = xy³

Video Explanation

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Solution

Question: If two positive integers a and b are written as

a = x³ y²
b = x y³

where x and y are prime numbers, then find HCF(a, b).

(a) xy    (b) xy²    (c) x³y³    (d) x²y²

Step 1: Write Prime Power Forms

a = x³ × y²

b = x¹ × y³

Step 2: Rule for HCF

The HCF is obtained by taking the lowest power of each prime common to both numbers.

Step 3: Find Lowest Powers

Lowest power of x = 1

Lowest power of y = 2

Step 4: Write the HCF

HCF(a, b) = x¹ y²

= xy²

Final Answer

✔ HCF(a, b) = xy²

✔ Correct option: (b) xy²

Conclusion

Thus, by taking the lowest powers of the common prime factors, the HCF of the given numbers is xy².