Find the HCF of m = pq³ and n = p³q²

Video Explanation

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Solution

Question: If two positive integers m and n are expressible in the form

m = p q³
n = p³ q²

where p and q are prime numbers, find HCF(m, n).

Step 1: Write the Prime Power Forms

m = p¹ × q³

n = p³ × q²

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 = 2

Step 3: Write the HCF

HCF(m, n) = p¹ q²

= p q²

Final Answer

✔ HCF(m, n) = p q²

Conclusion

Thus, by taking the lowest powers of the common prime factors p and q, the HCF of the given numbers is p q².