The given question is related to finding the greater number out of two numbers whose product is given and the highest common factor (HCF) is also given. Let's solve it step by step.

Given:
Product of two numbers = 4107
HCF of the two numbers = 37

Step 1: Prime Factorization of 4107
To find the prime factorization of 4107, we divide it by prime numbers starting from 2 until we cannot divide any further. The prime factors of 4107 are:

4107 ÷ 3 = 1369
1369 ÷ 37 = 37

So, the prime factorization of 4107 is 3 × 37 × 37.

Step 2: Determining the Numbers
Now that we have the prime factorization, we can determine the two numbers whose product is 4107 and whose HCF is 37. Since the HCF is 37, one of the numbers should be a multiple of 37. Let's assign the factors as follows:

Number 1 = 37 × a
Number 2 = 37 × b

Multiplying the two numbers, we get:
Number 1 × Number 2 = (37 × a) × (37 × b) = 4107

Expanding the equation:
(37 × 37) × (a × b) = 4107

Simplifying:
1369 × (a × b) = 4107

Dividing by 1369 on both sides:
a × b = 3

Step 3: Finding the Greater Number
We need to find the greater number out of the two. To do this, we need to consider the values of a and b. Since a and b are positive integers and their product is 3, the possible values for a and b are:

a = 1, b = 3
a = 3, b = 1

Substituting the values back into the equation, we get the two numbers:

Number 1 = 37 × a = 37 × 1 = 37
Number 2 = 37 × b = 37 × 3 = 111

Comparing the two numbers, we can see that the greater number is 111.

Therefore, the correct answer is option C) 111.