For the product of a multiplication fact to have the digit 4 in the ones place, we can analyze the situation based on the properties of multiplication and the possible digits that can appear at the ones place.
The numbers that can give a product with 4 in the ones place are:
- 2 (because 2 multiplied by 2 gives 4)
- 4 (because 4 multiplied by any even number results in a product ending with 4)
- 6 (because 6 multiplied by any even number results in a product ending with 4)
- 8 (because 8 multiplied by 3 gives 24, which has 4 in the ones place)
Among the given options (0, 2, 5, 10), let's analyze them:
- 0: \(0\) multiplied by anything gives \(0\), so it can't lead to a product ending in 4.
- 2: \(2\) multiplied by an even number can yield a product ending with 4 (for example, \(2 \times 2 = 4\)).
- 5: \(5\) multiplied by anything gives products ending in either 0 or 5, so it can’t lead to a product ending with 4.
- 10: \(10\) multiplied by anything gives a product that ends in 0, so it can't lead to a product ending with 4.
Therefore, the only factor among the options provided that must be one of the factors is:
2.