If 3147m9744 is a nine-digit number divisible by both 8 and 9, then find m

To find the value of 'm', we need to consider the rules of divisibility for 8 and 9.

1. A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
2. A number is divisible by 9 if the sum of its digits is divisible by 9.

Let's apply these rules to the given number 3147m9744.

1. For the number to be divisible by 8, 'm74' should be divisible by 8. The numbers that can be formed by replacing 'm' with digits from 0 to 9 and are divisible by 8 are 074, 174, 274, 374, 474, 574, 674, 774, 874, and 974. So, the possible values for 'm' considering divisibility by 8 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

2. For the number to be divisible by 9, the sum of its digits should be divisible by 9. The sum of the known digits is 3+1+4+7+9+7+4+4 = 39. If we add 'm' to this sum, the result should be divisible by 9. The only possible values for 'm' that make the sum divisible by 9 are 0 and 9.

Considering both conditions, the only common value for 'm' is 0. So, 'm' should be 0 for the number 3147m9744 to be divisible by both 8 and 9.