Question

if two positive integers m and n are expressible in the form of m=pq^3 anc n=p^3q^2, where p,q are prime numbers, then HCF(m,n)=​

Answer 1

HCF is pq²

HCF is the common number in it's lowest term

Answer 2

The value of HCF(m,n) is pq².

Step-by-step explanation:

The HCF of any two number a and b is the highest common factor that divides both number a and b.

Given : Two positive integers m and n are expressible in the form of $m=pq^3$and  $n=p^3q^2$, where p,q are prime numbers.

Prime Factorization of m = $p \times q\times q\times q$  [∵p,q are prime numbers]

Prime Factorization of n = $p \times p\times p\times q\times q$ [∵p,q are prime numbers]

Highest common factor of m and n : HCF (m,n)= $p \times q\times q = pq^2$

Hence, the HCF(m,n)=​ pq².

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