15?1792 is divisible by 9 only when ?=

Step-by-Step Solution

To determine the missing digit (represented by '?') such that the number 15?1792 is exactly divisible by 9, we apply the sum of digits rule: a number is divisible by 9 if and only if the sum of its digits is a multiple of 9 (e.g., 9, 18, 27, 36...).

1. Sum the known digits:

   • Known digits are 1, 5, 1, 7, 9, 2.

   • Sum = 1 + 5 + 1 + 7 + 9 + 2 = 25.

2. Set up the equation with the unknown digit (?):

   • Let '?' be represented by 'x'.

   • The total sum of digits = 25 + x.

3. Find the smallest multiple of 9 greater than 25:

   • Multiples of 9 are 9, 18, 27, 36...

   • The smallest multiple of 9 that is greater than 25 is 27.

4. Solve for x:

   • 25 + x = 27

   • x = 27 - 25

   • x = 2.

Therefore, the missing digit is 2.