Correct Answer - Option 1 : 14

**Given:**

H.C.F(35, 75) = x - y

And, 2x + y = 16

**Calculation:**

As, 35 = 5 × 7

And, 75 = 3 × 5 × 5

So, H.C.F(35, 75) = 5

And, ATQ

x - y = 5 ----(1)

And, 2x + y = 16 ----(2)

Solving equations (1) and (2), we get

3x = 21

⇒ x = 7

And, from (1)

⇒ 7 - y = 5

⇒ y = 7 - 5 = 2

Now, xy = 7 × 2 = 14

**∴ The value of xy is 14.**

The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor.

It is also called the Greatest Common Measure(GCM) and Greatest Common Divisor(GCD).