On the GMAT, problems about factors are constrained to POSITIVE factors.
The problem above would probably read as follows:
How many different POSITIVE INTEGERS are factors of 50?
a)3
b)4
c)5
d)6
6)8
Factor pairs of 50:
1*50
2*25
5*10
6 different factors.
The correct answer is
D.
An alternate way to count the number of positive factors of an integer:
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
For example:
72 = 2³ * 3².
Adding 1 to each exponent and multiplying, we get (3+1)*(2+1) = 12 factors.
Here's the reasoning. To determine how many factors can be created from 72 = 2³ * 3², we need to determine the number of choices we have of each prime factor:
For 2, we can use 2�, 2¹, 2², or 2³, giving us 4 choices.
For 3, we can use 3�, 3¹, or 3², giving us 3 choices.
Multiplying, we get 4*3 = 12 possible factors.
In the problem above:
50 = 2¹*5².
Adding 1 to each exponent and multiplying, we get:
(1+1)(2+1) = 6 different factors.
Similar problems:
https://www.beatthegmat.com/divisors-t85731.html
https://www.beatthegmat.com/all-factors- ... 15019.html
https://www.beatthegmat.com/if-n-has-15- ... 64736.html
A problem about counting only the ODD factors:
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