Given:

The number 35a246772 is in base 9.

The number when written in base 10 is divisible by 8.

We need to find the value of digit a.


Approach:

To find the value of digit a, we need to convert the number from base 9 to base 10 and check if it is divisible by 8.

The conversion from base 9 to base 10 can be done by multiplying each digit of the number with the corresponding power of 9 and summing them up.

If the resulting number is divisible by 8, then the value of digit a will satisfy the given condition.


Conversion from Base 9 to Base 10:

To convert the number 35a246772 from base 9 to base 10, we can use the following formula:

Number in base 10 = (3 * 9^9) + (5 * 9^8) + (a * 9^7) + (2 * 9^6) + (4 * 9^5) + (6 * 9^4) + (7 * 9^3) + (7 * 9^2) + (2 * 9^1)

Simplifying this expression gives:

Number in base 10 = 387420489 + 2952450a + 78732 + 13122 + 26244 + 4374 + 567 + 81 + 18

Number in base 10 = 387426705 + 2952450a


Checking Divisibility by 8:

To check if the number in base 10 is divisible by 8, we need to divide it by 8 and see if the remainder is 0.

Let's divide the number by 8:

387426705 + 2952450a = 8 * 48428338 + 2952450a

The remainder is 2952450a.

Since the given number is divisible by 8, the remainder should be 0.

Thus, we have the equation 2952450a = 0.

The only value of a that satisfies this equation is a = 0.


Conclusion:

The value of digit a in the number 35a246772, when written in base 9, is 0.