SOLUTION: for how many positive integers x is 130/x an integer? a.8 b.7 c.6 d.d

The integer number 130 has this decomposition into the product of these prime numbers:

130 = .. = ...


Note that the indexes are 1 for 2, 1 for 5 and 1 for 13.


Now add 1 to each of the three indexes:

1 + 1 = 2  (for 2);

1 + 1 = 2  (for 5);

1 + 1 = 2  (for 13).


Now the number of all divisors for 130 (including 1 and including 130 itself) is the product 2*2*2 = 8.


They are

1   = ,

2   = ,

5   = ,

10  = ,

13  = ,

26  = ,

65  = ,

130 = .