The product of two numbers is 2028 and their HCF is 13. How many pairs of such numbers are possible?Options :A.1B.2C.3D.4

The solution to this problem involves understanding the relationship between the Highest Common Factor (HCF) and the product of two numbers.

Step 1: We know that the product of two numbers is equal to the product of their HCF and their Lowest Common Multiple (LCM).

Step 2: In this case, we know that the product of the two numbers is 2028 and their HCF is 13. Therefore, their LCM is 2028/13 = 156.

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

Step 4: However, we need to consider only those pairs where the HCF is 13. The HCF of (1,156), (2,78), (3,52), (4,39), (6,26) is not 13. The HCF of (12,13) is 13.

Therefore, there is only 1 pair of such numbers possible. So, the answer is A.1.