Carcass wrote:
How many unique factors does the number 54 have?
A. Six
B. Seven
C. Eight
D. Nine
E. Ten
----------ASIDE----------------------------------------
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
---ONTO THE QUESTION!--------------------------------
54 = (2)(3)(3)(3)
= (2^
1)(3^
3)
So, the number of positive divisors of 54 = (
1+1)(
3+1) =(2)(4) =
8Answer: C
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ALTERNATIVELY, we can just list all of the factors to get: {1, 2, 3, 6, 9, 18, 27, 54}
8 factors
Answer: C