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Updated on: 01 Dec 2016, 02:01
Originally posted by MathRevolution on 29 Nov 2016, 17:37.
Last edited by MathRevolution on 01 Dec 2016, 02:01, edited 1 time in total.
Last edited by MathRevolution on 01 Dec 2016, 02:01, edited 1 time in total.
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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:
5%
(low)
Question Stats:
86% (00:50) correct
14%
(01:33)
wrong
based on 120
sessions
History
Date
Time
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Not Attempted Yet
If \(n=2^5*3^4*5^3*7^2*11\), how many factors of n are there?
A. 180 B. 360 C. 540 D. 720 E. 810
A. 180 B. 360 C. 540 D. 720 E. 810
29 Nov 2016, 17:49
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Number of factors of any positive integer of the form \(k=p^a*q^b*r^c\) where p,q,r are prime number is given by the equation => \((a+1)*(b+1)*(c+1)\)
Hence the number of factors => 6*5*4*3*2
For quick calculation notice the above value is 6! and the value of 6! is 720
Hence D
Side Note =>
Its good if you know the fist few factorials =>
1!->1
2!->2
3!->6
4!->24
5!->120
6!->720
Additionally 0!->1
Hence the number of factors => 6*5*4*3*2
For quick calculation notice the above value is 6! and the value of 6! is 720
Hence D
Side Note =>
Its good if you know the fist few factorials =>
1!->1
2!->2
3!->6
4!->24
5!->120
6!->720
Additionally 0!->1
01 Dec 2016, 02:00
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==> The number of factors become (5+1)(4+1)(3+1)(2+1)(1+1)=720, and therefore the answer is D.
Answer: D
Answer: D
