The product of two numbers is 2028 and their HCF is 13. How many pairs of such numbers are possible?

Sure, here is the step by step solution:

Step 1: We know that the product of two numbers is equal to the product of their HCF and LCM. So, the LCM of the two numbers is 2028/13 = 156.

Step 2: Now, we need to find the pairs of numbers whose LCM is 156. The pairs of factors of 156 are (1,156), (2,78), (3,52), (4,39), (6,26), (12,13).

Step 3: However, since the HCF of the two numbers is 13, we need to find the pairs whose HCF is 13. The only pairs that satisfy this condition are (1,156) and (12,13).

Step 4: But, we need to consider that the numbers could be in either order, so each pair actually represents two pairs of numbers. Therefore, there are 2*2 = 4 pairs of such numbers.

So, there are 4 pairs of such numbers possible.