If the product and H.C.F. of two numbers are 4107 and 37 respectively, then…

To find the numbers when you know their product and their Highest Common Factor (H.C.F.), we use the fact that any two numbers can be written as multiples of their H.C.F.

The Concept

Let the two numbers be H × x and H × y, where H is the H.C.F. and x and y are co-prime numbers (they have no common factors).

• Product of the two numbers = (H × x) × (H × y) = H² × (x × y)

Step-by-Step Calculation

1. Identify given values:

   • H.C.F. (H) = 37

   • Product = 4107

2. Set up the equation:

   • 37² × (x × y) = 4107

   • 1369 × (x × y) = 4107

3. Find the product of the co-prime factors (x × y):

   • x × y = 4107 / 1369 = 3

4. Determine the co-prime factors:

   • The only factors of 3 are 1 and 3. So, x = 1 and y = 3.

5. Calculate the original numbers:

   • First number = H × x = 37 × 1 = 37

   • Second number = H × y = 37 × 3 = 111

6. Find the greater number:

   • Comparing 37 and 111, the greater number is 111.