The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then…

To find the greater of two numbers when their product and Highest Common Factor (HCF) are known, we use the property that any two numbers sharing an HCF can be represented as multiples of that HCF.

Step-by-Step Calculation
1. Represent the numbers:
Let the HCF be H = 37. The two numbers can be written as:
Number 1 = 37 * a
Number 2 = 37 * b
(Where a and b are coprime—they have no common factors other than 1.)

2. Use the product information:
The product of the two numbers is given as 4107.
(37 * a) * (37 * b) = 4107
1369 * (a * b) = 4107
a * b = 4107 / 1369
a * b = 3

3. Find the coprime factors:
The only factors of 3 are 1 and 3. Since 1 and 3 are coprime, our values for a and b are 1 and 3.

4. Determine the numbers:
Number 1 = 37 * 1 = 37
Number 2 = 37 * 3 = 111

The two numbers are 37 and 111. The greater number is 111.