To find the number of two-digit positive integers where the product of their digits equals 24, we start by identifying the two digits of a two-digit number, which we can denote as AB, where A is the tens digit and B is the units digit.
Given that the product of the digits is stated as:
A × B = 24
Since A is the tens digit, it must be one of the numbers from 1 to 9, and B can be any digit from 0 to 9. Therefore, we need to find pairs of digits (A, B) such that their product is 24, and both numbers fall within the applicable range for two-digit integers.
Let’s find the pairs:
- 1. (3, 8) → 38 (because 3 × 8 = 24)
- 2. (4, 6) → 46 (because 4 × 6 = 24)
- 3. (6, 4) → 64 (because 6 × 4 = 24)
- 4. (8, 3) → 83 (because 8 × 3 = 24)
Checking the valid pairs once again:
- 3 × 8 = 24, yielding the number 38
- 4 × 6 = 24, yielding the number 46
- 6 × 4 = 24, yielding the number 64
- 8 × 3 = 24, yielding the number 83
Therefore, we conclude that there are a total of four two-digit positive integers where the product of their digits equals 24:
- 38
- 46
- 64
- 83
In summary, the total number of two-digit positive integers such that the product of their digits is 24 is 4.