If the number 24753x is completely divisible by 72 then which of the following numbers should replace x(a) 4(b) 5(c) 6(d) 7

To determine which number should replace x in the number 24753x to make it completely divisible by 72, we need to find the factors of 72 and then check which of the given options (a) 4, (b) 5, (c) 6, or (d) 7 makes the entire number divisible by 72.

First, let's find the prime factorization of 72:

72 = 2^3 * 3^2

Now, to be divisible by 72, the number 24753x should also have these prime factors in the same or higher powers.

Let's analyze the options:

(a) 4: 247534 is divisible by 2^3 * 3^2, which is 72. So, if x is replaced by 4, it will be divisible by 72.

(b) 5: 247535 is not divisible by 72 because it doesn't have enough 2s and 3s in its prime factorization.

(c) 6: 247536 is divisible by 2^3 * 3^2, which is 72. So, if x is replaced by 6, it will be divisible by 72.

(d) 7: 247537 is not divisible by 72 because it doesn't have enough 2s and 3s in its prime factorization.

So, the correct answer is (a) 4. If x is replaced by 4, the number 247534 will be completely divisible by 72.