Explanation

We are given:

• H.C.F (Highest Common Factor) = 12

• Difference between the two numbers = 12

  Step-by-step method:

Let the two numbers be:
x and x + 12

Since H.C.F = 12, both numbers must be divisible by 12.

Let’s assume:

$$x=12a\text{and}x+12=12b$$

So,

$$x+12-x=12b-12a=12(b-a)=12\Rightarrow b-a=1$$

So:

$$a=k,b=k+1\Rightarrow \text{The numbers are }12k\text{ and }12(k+1)$$

Try k = 7:

$$12 × 7 = 84,quad 12 × 8 = 96 Rightarrow text{Numbers are } 84 text{ and } 96$$

• Difference: $96-84=12$ 

• H.C.F of 84 and 96 is 12