To determine how many two-digit positive integers have a product of 24, we first need to identify the pairs of factors that multiply to 24. The two-digit integers are from 10 to 99.
Let’s examine the pairs of integers that multiply to 24:
- (1, 24)
- (2, 12)
- (3, 8)
- (4, 6)
Now we need to check which of these factor pairs consist of two-digit integers:
- 1 and 24: Not applicable, since 1 is not a two-digit number.
- 2 and 12: Not applicable, since 2 is not a two-digit number.
- 3 and 8: Not applicable, since 3 and 8 are not two-digit numbers.
- 4 and 6: Not applicable, since 4 and 6 are not two-digit numbers.
Looking at these pairs, we note that none of the factors can be considered two-digit numbers. Therefore, the answer is that there are zero two-digit positive integers whose product is 24.
In conclusion, the total number of two-digit positive integers whose product equals 24 is 0.