Question

Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?
350
700
1050
525
​

Answer 1

x=525,y=525 hence hcf between is 525.

Answer 2

Given,

The sum of the two numbers which is x and y is 1050.

To Find,

The maximum value of the HCF between x and y.

Solution,

The given mathematical problem will be solved by assuming a highest common factor of x and y.

Let x = h × a

Let y = h × b

Where h is assumed to be the highest common factor of x and y.

The question states that,

⇒ x + y = 1050

Substituting the assumed values of x and y we get,

⇒ h × a + h × b = 1050

⇒ h (a + b) = 1050

To maximize h, we need to minimize a + b and as we know that a and b are positive integers. Therefore, the least value or minimum possible value of  a + b is 2.

∴ h = 1050/2

⇒ h = 525

Hence, the maximum value of HCF between x and y is 525.