For what value of M, 859M is divisible by 9?

To find the value of M that makes the number 859M divisible by 9, we must apply the divisibility rule for 9.

Divisibility Rule for 9
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, etc.).

Calculation Steps
Identify the sum of the known digits:
The number is 859M. The known digits are 8, 5, and 9.
Sum = 8 + 5 + 9 = 22

Set up the equation for divisibility:
We need the total sum of digits (22 + M) to be a multiple of 9.

The next multiple of 9 after 22 is 27.

22 + M = 27

M = 27 - 22

M = 5

Verification:
If M = 5, the number becomes 8595.
Sum of digits = 8 + 5 + 9 + 5 = 27.
Since 27 is divisible by 9, the number 8595 is also divisible by 9.