The product of two numbers is 2028 and HCF is 13. The number of such pairs area.2b.3c.5d.4

The problem is asking for the number of pairs of two numbers that have a product of 2028 and a Highest Common Factor (HCF) of 13.

Step 1: We know that the product of two numbers is equal to the product of their HCF and LCM (Lowest Common Multiple). So, if the product of the numbers is 2028 and the HCF is 13, then the LCM is 2028/13 = 156.

Step 2: 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 the divisors of 156.

Step 3: The divisors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.

Step 4: We can pair these divisors up into pairs that multiply to 156: (1,156), (2,78), (3,52), (4,39), (6,26), (12,13).

Step 5: However, we need to remember that the HCF of our numbers is 13. This means that 13 must be a factor of our numbers. Looking at our pairs, we see that the pairs (1,156), (2,78), (12,13) include 13 as a factor.

So, there are 3 pairs of numbers that have a product of 2028 and a HCF of 13. Therefore, the answer is b.3.