How many factors does 36^2 have?
2
8
24
25
26
I chose B (8) based on that it breaks down to four:2's and four:3's. Why is the explanation stating that you have 5 × 5 = 25 different ways to construct a factor, which makes complete sense but I suppose I didn't really understand what the question was asking for..? How would one know to do this on test day instead of picking the obvious B (8)?
Manhattan PS
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To determine the number of positive factors of an integer:How many factors does 36^2 have?
a.2
b.8
c.24
d.25
e.26
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
36² = 2�3�.
Adding 1 to each exponent and multiplying, we get:
(4+1)(4+1) = 25 factors.
The correct answer is D.
Here's the reasoning:
To determine how many factors can be created from 36² = 2�3�, we need to determine the number of choices we have of each prime factor:
For 2, we can use 2�, 2¹, 2², 2³, or 2�, giving us 5 choices.
For 3, we can use 3�, 3¹, 3², 3³, or 3�, giving us 5 choices.
To combine the number of choices we have of each prime factor, we multiply:
5*5 = 25 factors.
Similar problems:
https://www.beatthegmat.com/divisors-t85731.html
https://www.beatthegmat.com/all-factors- ... 15019.html
A problem about counting only the ODD factors:
https://www.beatthegmat.com/gmat-loves-f ... 72876.html
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