Question

The sum of two numbers is 187 and their hcf is 17. what is the number of such pairs of numbers satisfying the above condition

Answer 1

x = 17*a
y = 17*b
such that HFC(a,b)=1 (because x,y have no common factor bigger than 17)
We also know that x+y=187
Hence, a+b = 187 / 17 = 11

Therefore, assuming a reasonable (but not specified in your question) constraint that x,y are positive, (a,b) may be (1,10), (2,9),(3,8),(4,7),(5,6).
All of these pairs are co-prime (having HFC equal to 1), hence their HCF is 17 like you requested.

Hence there are 5 possible pairs of integers (x,y) that satisfy your restrictions (and you can also switch the roles of x and y to have 10 pairs, if order does NOT matter)

Answer 2

Concept introduction:

Highest Common Factor is the acronym for this term. The highest factor that may divide two integers evenly is known as the HCF of two numbers. HCF can be assessed using two or more numbers. It is the most powerful divisor for any pair of integers that can divide the inputted numbers equally or fully.

Given:

Here it is given that the sum of two numbers is $187$ and their hcf is $17.$

To find:

We have to find the two numbers.

Solution:

According to the question, the sum of two numbers is $187$ and their hcf is $17.$

So, the numbers are must be the multiplier value of $17$.

So, the numbers are must be

$17*5=85\\17*6=102$    because if we add those two numbers we get the value $187$ which is given to us.

Final answer:

Hence, the numbers are $85$ and $102$ and this is our final answer.

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