ardz24 wrote:The positive integer 200 has how many factors?
A. 2
B. 10
C. 12
D. 15
E. 24
I'm confused how to set up the formulas here. Can any experts help?
APPROACH #1 - FORMULA
If the
prime factorization of N = (p^
a)(q^
b)(r^
c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (
a+1)(
b+1)(
c+1)(etc) positive divisors.
Example: 14000 = (2^
4)(5^
3)(7^
1)
So, the number of positive divisors of 14000 = (
4+1)(
3+1)(
1+1) =(5)(4)(2) = 40
Now onto the question...
Example: 200 = (2^
3)(5^
2)
So, the number of positive divisors of 200 = (
3+1)(
2+1)
= (4)(3)
= 12
= C
APPROACH #2 - LIST
We can quickly list all of the factors of 200
I suggest we do so in PAIRS of values whose product is 200
We get:
1 and 200
2 and 100
4 and 50
5 and 40
8 and 25
10 and 20
DONE!
Total = 12
= C
Cheers,
Brent
