Complete the Composite Number: Fill in the Blank for _7

To solve this problem of finding a composite number in the form of "$\square7$", let's evaluate each of the given digit choices:

• Choice 1: Place 3 in front of 7, forming 37. Check divisibility:
  • 37 is only divisible by 1 and 37. Thus, 37 is a prime number, not a composite number.
• Choice 2: Place 7 in front of 7, forming 77. Check divisibility:
  • 77 is divisible by 1, 7, 11, and 77. Thus, 77 is a composite number (divisors: 1, 7, 11, 77).
  The formation $77$ verifies as composite.
• Choice 3: Place 4 in front of 7, forming 47. Check divisibility:
  • 47 has its only positive divisors as 1 and 47, implying it is a prime number, not a composite.
• Choice 4: Place 6 in front of 7, forming 67. Check divisibility:
  • 67's divisors beyond 1 are 67 only, making it a prime number, not composite.

Given the analysis of each possible number formed, the only composite number is $77$. Therefore, placing a 7 in front of 7 achieves the objective.

Thus, the correct filling digit resulting in a composite number is $7$.