Sum of two numbers is 16 and their HCF is 4. A denotes the greater of the two numbers, find the value of A.

Let's denote the two numbers as A and B. Given that the sum of the two numbers is 16, we can write this as:

A + B = 16

We also know that the highest common factor (HCF) of the two numbers is 4. This means that both A and B are divisible by 4.

Let's denote the other factors of A and B (apart from 4) as x and y respectively. So we can write:

A = 4x B = 4y

Substituting these into the first equation gives:

4x + 4y = 16 x + y = 4

Since A is the greater of the two numbers, x must be greater than y. The possible pairs of (x, y) that satisfy the equation x + y = 4 are (1, 3), (2, 2), and (3, 1). But since x must be greater than y, the only possible pair is (3, 1).

So, x = 3 and y = 1. Substituting x = 3 into the equation A = 4x gives:

A = 4 * 3 = 12

So, the value of A is 12.