To find the largest value of n such that 6 divides the product of the first 100 natural numbers, we need to determine the highest power of 2 and 3 that divides the product.

First, let`s look at the highest power of 2. We know that 6 = 2 * 3. Since 2 is a prime factor of 6, the highest power of 2 that divides the product is determined by counting the number of multiples of 2 in the product.

To calculate this, we use the formula for the sum of an arithmetic series: n/2 * (first term + last term). In this case, the first term is 2 and the last term is 100. So, the sum of multiples of 2 would be (100/2) * (2 + 100), which simplifies to 50 * 102. Therefore, the highest power of 2 that divides the product is 2^50.

Next, let`s look at the highest power of 3. Similarly, we count the number of multiples of 3 in the product. Again using the formula for the sum of an arithmetic series, the sum of multiples of 3 would be (100/3) * (3 +