If 604___6 is divisible by 11, then the integer in the blank space is

A number is divisible by 11 exactly when the difference between the sum of its digits at odd positions and the sum of its digits at even positions (counted from either end) is 0 or a multiple of 11.

1. Label the digits of 604x6 by position: 6 (1st), 0 (2nd), 4 (3rd), x (4th), 6 (5th).

2. Sum the digits at the odd positions (1st, 3rd, 5th): 6 + 4 + 6 = 16.

3. Sum the digits at the even positions (2nd, 4th): 0 + x = x.

4. Set the alternating sum to a multiple of 11: 16 - x = 11k for some integer k.

5. Since x is a single digit (0 to 9), 16 - x lies between 7 and 16; the only multiple of 11 in that range is 11, so 16 - x = 11, giving x = 5.

Cross-check: substituting x = 5 gives the number 60456; dividing, 60456 / 11 = 5496 exactly (5496 x 11 = 60456), confirming divisibility by 11.

So the missing digit is 5.