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**Hint:**Divisibility rule of 8: - Last three-digit of number should be divisible by 8 then the whole number is divisible by 8.

Divisibility rule of 9: -

The Sum of all digits of a number should be multiple of 9 or divisible by 9.

**Complete step-by-step solution:**We will first of all factor 72.

Since 72 is a composite number it has more than 2 factors.

8 and 9 are coming under factors of 72.

So for any number to be divisible by 72, it should be divisible by 9 & 8.

Now we will study the divisible rules of 8 and 9.

Divisibility rule of 8: -

The last three digits of the number should be divisible by 8 then the whole number is divisible by 8.

Divisibility rule of 9: -

The Sum of all digits of a number should be multiple of 9 or divisible by 9.

Now we have the number as 24753x.

Sum is 2 + 4 + 7 + 5 + 3 + x, for it to be divisible by 9 we must have, sum = multiple of 9.

\[\Rightarrow \] 2 + 4 + 7 + 5 + 3 + x = multiple of 9.

\[\Rightarrow \] 21 + x = multiple of 9.

Now we will consider all options separately.

Option (a), Let x = 4,

\[\Rightarrow \] 21 + 4 = 25, not a multiple of 9.

So, option (a) is correct.

Option (b), Let x = 5.

\[\Rightarrow \] 21 + 5 = 26, not a multiple of 9.

So, option (b) is incorrect.

Option (c), Let x = 6.

\[\Rightarrow \] 21 + 6 = 27, yes a multiple of 9.

So, option (c) is correct.

Option (d), Let x = 7, then,

\[\Rightarrow \] 21 + 7 = 28, not a multiple of 9.

Wrong option.

Also when x = 6, then the last three digits of 24753x are 536 which is divisible by 8.

**So, x = 6 is correct answer which is option (c).**

**Note:**Another way to solve this question can be checked for divisibility of 8 on all options. That can be long but will anyway give the same result.

Option (a), let x = 4

Then 247534 has last three-digit as 534.

Clearly, \[\dfrac{534}{8}=66.75\].

So, 534 is not divisible by 8.

Hence option (a) is wrong.

Option (b), let x = 5

Then 247535 has the last three digits as 535.

Clearly, \[\dfrac{535}{8}=66.87\].

So, 535 is not divisible by 8.

Option (b) is wrong.

Option (c), let x = 6

Then 247536 has the last three digits as 536.

Clearly, \[\dfrac{536}{8}=67\].

So, 536 is divisible by 8.

Hence option (c) is correct.

Option (d), let x = 7.

Then 537 is not divisible by 8.

Option (d) wrong.

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