Find the HCF of a = pq² and b = p³q

Video Explanation

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Solution

Question: If two positive integers a and b are expressible in the form

a = p q²
b = p³ q

where p and q are prime numbers, find HCF(a, b).

Step 1: Write Prime Powers

a = p¹ × q²

b = p³ × q¹

Step 2: Apply the Rule for HCF

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

Lowest power of p = 1

Lowest power of q = 1

Step 3: Write the HCF

HCF(a, b) = p¹ q¹

= p q

Final Answer

✔ HCF(a, b) = p q

Conclusion

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