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Updated on: 12 Aug 2023, 05:04
Originally posted by guerrero25 on 11 Feb 2013, 01:26.
Last edited by Bunuel on 12 Aug 2023, 05:04, edited 3 times in total.
Last edited by Bunuel on 12 Aug 2023, 05:04, edited 3 times in total.
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E
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Difficulty:
15%
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Question Stats:
78% (00:44) correct
22%
(01:16)
wrong
based on 384
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How many positive integers are factors of 90?
A. 6
B. 8
C. 9
D. 10
E. 12
M02-24
A. 6
B. 8
C. 9
D. 10
E. 12
M02-24
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11 Feb 2013, 01:44
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How many positive integers are factors of 90?
A. 6
B. 8
C. 9
D. 10
E. 12
Determining the Number of Positive Factors of a Positive Integer \(n\):
First, perform the prime factorization of an integer \(n\). Let \(n = p^a * q^b * r^c\), where \(p\), \(q\), and \(r\) are the prime factors of \(n\), and \(a\), \(b\), and \(c\) are their respective powers.
The number of positive factors of \(n\) can be determined by the formula \((a+1)(b+1)(c+1)\). NOTE: This includes 1 and \(n\) itself.
For example, to find the number of positive factors of 450, we first perform its prime factorization: \(450 = 2^1 * 3^2 * 5^2\). The total number of positive factors of 450, including 1 and 450, is \((1+1)(2+1)(2+1) = 18\) positive factors.
According to the above, 90, which is equal to \(2*3^2*5\), has \((1+1)(2+1)(1+1) = 12\) positive factors, namely 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Answer: E
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Hope it helps.
A. 6
B. 8
C. 9
D. 10
E. 12
Determining the Number of Positive Factors of a Positive Integer \(n\):
First, perform the prime factorization of an integer \(n\). Let \(n = p^a * q^b * r^c\), where \(p\), \(q\), and \(r\) are the prime factors of \(n\), and \(a\), \(b\), and \(c\) are their respective powers.
The number of positive factors of \(n\) can be determined by the formula \((a+1)(b+1)(c+1)\). NOTE: This includes 1 and \(n\) itself.
For example, to find the number of positive factors of 450, we first perform its prime factorization: \(450 = 2^1 * 3^2 * 5^2\). The total number of positive factors of 450, including 1 and 450, is \((1+1)(2+1)(2+1) = 18\) positive factors.
According to the above, 90, which is equal to \(2*3^2*5\), has \((1+1)(2+1)(1+1) = 12\) positive factors, namely 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Answer: E
Similar questions to practice:
https://gmatclub.com/forum/how-many-odd ... 06082.html
https://gmatclub.com/forum/how-many-fac ... 26422.html
https://gmatclub.com/forum/how-many-dif ... 30628.html
https://gmatclub.com/forum/how-many-dis ... 44326.html
Hope it helps.
General Discussion
27 Jul 2015, 03:41
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Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?
2^ 1 ∗3^ 2 ∗5^ 1 =90
therefore, for perfect square, we need to eliminate the identical factors?
Thanks in advance.
2^ 1 ∗3^ 2 ∗5^ 1 =90
therefore, for perfect square, we need to eliminate the identical factors?
Thanks in advance.
