Multiplied several natural numbers and got 224, and the smallest number was exactly half of the largest.

How many numbers were multiplied?

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$224=2^{5} \cdot 7$. Consider the two numbers mentioned in the condition: the smallest and the largest. If one of them is divisible by 7, then the other must also be divisible by 7. But 224 is not divisible by $7^{2}$, so both of these numbers must be powers of two. From the condition, it also follows that these are two consecutive powers of the number 2. In addition, the largest number must be greater than 7. Therefore, it is $2^{3}=8$, and the smallest is $2^{2}=4$. The only remaining factor is seven, so the required numbers are three: 4, 7, and 8.

## Answer

Three numbers.