To find the number of natural numbers greater than 7,00,000 that can be formed using the digits 0, 3, 5, 6, 7, 8 without repetition, we need to consider the positions of the digits in the number.

Number of options for the first digit:
Since the number should be greater than 7,00,000, the first digit cannot be 0. Therefore, we have 5 options for the first digit (3, 5, 6, 7, 8).

Number of options for the second digit:
Since repetition is not allowed and we have already used one digit, we have 5 options for the second digit.

Number of options for the third digit:
Similarly, we have 4 options for the third digit.

Number of options for the fourth digit:
Again, we have 3 options for the fourth digit.

Number of options for the fifth digit:
Similarly, we have 2 options for the fifth digit.

Number of options for the sixth digit:
Finally, we have 1 option for the sixth digit.

Using the multiplication principle, the total number of natural numbers greater than 7,00,000 that can be formed is:
5 x 5 x 4 x 3 x 2 x 1 = 600

However, we need to consider the fact that the number should be greater than 7,00,000.
The numbers formed by using 0 as the first digit will not be greater than 7,00,000. Therefore, we need to subtract the number of such numbers.

Number of options for the second digit (when the first digit is 0):
Since repetition is not allowed and we have already used one digit (0), we have 4 options for the second digit.

Number of options for the third digit:
Similarly, we have 3 options for the third digit.

Number of options for the fourth digit:
Again, we have 2 options for the fourth digit.

Number of options for the fifth digit:
Finally, we have 1 option for the fifth digit.

Using the multiplication principle, the total number of natural numbers formed by using 0 as the first digit is:
4 x 3 x 2 x 1 = 24

Therefore, the total number of natural numbers greater than 7,00,000 that can be formed without repetition is:
600 - 24 = 576

However, we need to consider that the question asks for the number of natural numbers, which includes 0 as well. Therefore, we need to add 1 to the result.

Final answer: 576 + 1 = 577

However, the given options do not include the answer 577. The closest option is 240, which seems to be an error. The correct answer should be none of the given options.