Answer:
6
Step-by-step explanation:
105 is a composite number (not prime). If you decompose 105 into its prime factors (see attached image), you get 105 = 3 x 5 x 7. This means that the product 105 can only be written this way; any other way, for example 15 x 7 would not use numbers that are single digits.
The question boils down to how many ways the digits 3, 5, 7 can be arranged, using each digit exactly once.
That's a permutation problem, and it can be answered easily by thinking this way: given the digits 3, 5, 7, there are 3 choices for the first digit, then 2 for the second digit (for EACH of the first choices), then only 1 choice for the final digit.
3 x 2 x 1 = 6 ways that 3, 5, 7 can be arranged to make a 3-digit number. Here they are:
357, 375, 537, 573, 735, 753
