To find the larger of the two numbers, we need to find the numbers themselves. Let's break down the given information step by step:

Step 1: Understand the problem.
We are given two numbers and their H.C.F (Highest Common Factor) and two other factors of their L.C.M (Least Common Multiple). We need to find the larger of the two numbers.

Step 2: Understand the concepts.
H.C.F: The highest common factor or greatest common divisor is the largest number that divides two or more numbers without leaving a remainder.
L.C.M: The least common multiple is the smallest positive integer that is divisible by both numbers.

Step 3: Analyze the given information.
We are given:
H.C.F = 23
Two factors of L.C.M = 13 and 14

Step 4: Use the given information to find the numbers.
Let's assume the two numbers are x and y.

We know that:
H.C.F × L.C.M = Product of the two numbers
23 × L.C.M = x × y

We are also given two factors of the L.C.M, which are 13 and 14. Therefore, the L.C.M must be a multiple of both 13 and 14.

Step 5: Determine the L.C.M.
The L.C.M is the smallest multiple that is divisible by both 13 and 14. We can find the L.C.M using the prime factorization method.

Prime factorization of 13: 13
Prime factorization of 14: 2 × 7

To find the L.C.M, we take the highest power of each prime factor:
L.C.M = 2 × 7 × 13 = 182

Step 6: Find the numbers x and y.
Using the equation: 23 × L.C.M = x × y
23 × 182 = x × y
4196 = x × y

Now, we need to find two numbers whose product is 4196 and whose H.C.F is 23.

Step 7: Find the numbers using the H.C.F and product.
We can find the numbers by factorizing 4196 and checking which factors have an H.C.F of 23.

Prime factorization of 4196: 2 × 2 × 31 × 17

Factors of 4196:
1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108, 899, 1798, 3596, 4196

Among these factors, the ones with an H.C.F of 23 are 23 × 4 = 92 and 23 × 2 = 46.

Step 8: Determine the larger number.
The larger of the two numbers is 92.

Therefore, the correct answer is option 'C' - 322.