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29 Jan 2024, 08:27
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (00:49) correct
30%
(01:08)
wrong
based on 504
sessions
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Not Attempted Yet
If p and s are different prime numbers, how many different positive factors does \(ps^2\) have?
A. Two
B. Three
C. Five
D. Six
E. Seven
2024-01-29_19-22-01.png [ 24.52 KiB | Viewed 6698 times ]
A. Two
B. Three
C. Five
D. Six
E. Seven
Attachment:
2024-01-29_19-22-01.png [ 24.52 KiB | Viewed 6698 times ]
29 Jan 2024, 08:30
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guddo
If p and s are different prime numbers, how many different positive factors does \(ps^2\) have?
A. Two
B. Three
C. Five
D. Six
E. Seven
A. Two
B. Three
C. Five
D. Six
E. Seven
Attachment:
2024-01-29_19-22-01.png
Since p and s are different prime numbers, \(ps^2\) will have (1 + 1)(2 + 1) = 6 positive factors: 1, p, s, ps, s^2, ps^2.
Answer: D.
P.S Finding the Number of Factors of an Integer
First, make the prime factorization of an integer \(n = a^p * b^q * c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\), and \(p\), \(q\), and \(r\) are their respective powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and \(n\) itself.
Example: Finding the number of all factors of 450: \(450 = 2^1 * 3^2 * 5^2\)
The total number of factors of 450, including 1 and 450 itself, is \((1+1)(2+1)(2+1) = 2*3*3 = 18\) factors.
General Discussion
05 Feb 2024, 09:30
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Bunuel IF i take 3 and 5 as the two prime numbers then 5*3^2 = 225 , which has 5*5*3*3 , [ 2+ 1 ] [ 2+ 1 ] = 9 factors which is not in the option
