To fill in the blanks with the missing factors from the set {1, 2, __, 4, 6, __, 12, __, 21, 28, 42, 84}, we start by identifying the factors of 84, which are:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Now we can see which factors we already have and which are missing:
- The existing factors in the set are: 1, 2, 4, 6, 12, 21, 28, 42, 84.
- The factors we can fill in are: 3 (missing), 7 (missing), and 14 (missing).
So, filling in the blanks, the complete list will be:
{1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84}.
To summarize, the filled-in factors in the blanks are 3, 7, and 14.