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How many different positive integers are factors of 441 ? A
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14 Aug 2020, 10:51
14 Aug 2020, 10:51
Expert Reply
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Question Stats:
86% (00:54) correct
13% (01:00) wrong based on 30 sessions
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How many different positive integers are factors of 441 ?
A. 4
B. 6
C. 7
D. 9
E. 11
A. 4
B. 6
C. 7
D. 9
E. 11
Re: How many different positive integers are factors of 441 ? A
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14 Aug 2020, 10:51
14 Aug 2020, 10:51
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: How many different positive integers are factors of 441 ? A
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14 Aug 2020, 11:00
14 Aug 2020, 11:00
Carcass wrote:
How many different positive integers are factors of 441 ?
A. 4
B. 6
C. 7
D. 9
E. 11
A. 4
B. 6
C. 7
D. 9
E. 11
----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!!----------------------------
441 = (3)(3)(7)(7) = (3^2)(7^2)
So, the number of positive divisors of 441 = (2+1)(2+1)
= (3)(3)
= 9
Answer: D
Cheers,
Brent
