If the number 58579A is exactly divisible by 36, then what is the value of A?

To be divisible by 36, the number must be divisible by both 4 and 9 (since 4 × 9 = 36).

For divisibility by 4, the last two digits (9A) must be divisible by 4. Checking values, 92 and 96 are divisible by 4. So, A could be 2 or 6.

For divisibility by 9, the sum of digits (5 + 8 + 5 + 7 + 9 + A) = 34 + A must be divisible by 9.

If A = 2, sum = 36 (divisible by 9). However, we must check if 58792 is divisible by 36. 58792 ÷ 4 = 14698, but 14698 is not divisible by 9.

Let's re-check the calculation: If A = 4, 94 is not divisible by 4. Wait, the condition for 4 is the last two digits. Let's re-verify:

Divisibility by 4: 9A must be divisible by 4. Possible values: 92 (A=2) or 96 (A=6).

Sum of digits: 5+8+5+7+9+A = 34+A. For 34+A to be divisible by 9, A must be 2 (34+2=36).

Let's re-examine the number 5879A. If A=2, number is 58792. 58792/4 = 14698. 14698/9 = 1633.11 (Not divisible).

Let's check if the number was 58579A. Sum: 5+8+5+7+9+A = 34+A. For A=2, sum=36. 585792 / 36 = 16272. It is correct.
Final Answer: Option 1 (2)