This question asks: “What is the sum of the two smallest integers that are **NOT** factors of 20! and are also **NOT** prime numbers?”. The answer to this question is 104 which is obtained by the sum 46+58.

I think there are two problems with this question:

- There is no requirement that the two integers have to be positive. Other GregMat questions on the topic of factoring specify this restriction. Without this restriction, you can have a sum of infinitely small terms that are not factors of 20!.
- The question does not specify that the two integers have to be different. Since this restriction is not made, the sum of 46 and 46 is smaller than 104.