Question

if two positive integers A and B are written as a=p³q² andb=pq³ p and q are prime numbers then hcf (a,b)is​

Answer 1

Answer:

Given :

a = pq²& b = p³q, p & q are prime number.

The factors are as follows:

a = p¹ x q²

b = p³ x q¹

HCF (a,b) = pq²

Hence, p³q²

HCF= HCFof two or more numbers product of the greatest power of each common prime factor involved in the numbers with highest power.

hope it helps ✅✅

Answer 2

Given:

Two positive integers A and B are written as a=p³q² and b=pq³ where p and q are prime numbers.

To find:

The HCF (a, b).

Solution:

The HCF of given numbers a and b is pq².

To answer this question, we will follow the following steps:

First of all, we should know that the HCF of two numbers 'a' and 'b' is the highest common factor present in both numbers.

Now,

As given in the question, we have,

The number a = p³q² = pq²(p²)

The number b = pq³ = pq²(q)

where p and q are prime numbers.

So,

The highest common factor (HCF) present in numbers in a and b = pq²

Hence, the HCF of a and b is pq².