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 positive factors.
Here's why:
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 and to count the number of ways these choices can be combined:
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 the number of choices we have of each factor, we get 4*3 = 12 positive factors.
Mechmeera wrote:source Kaplan
How many positive factors does the positive integer x have?
(1) x is the product of 3 distinct prime numbers.
(2) x and 3� have the same number of positive factors.
Statement 1:
x = a¹b¹c¹, where a, b and c are distinct prime numbers.
Adding 1 to each exponent and multiplying, we get:
(1+1)(1+1)(1+1) = 8 positive factors.
SUFFICIENT.
Statement 2:
Since we can count the number of positive factors for 3�, the number of positive factors for x can be determined.
SUFFICIENT.
The correct answer is
D.
To determine the number of positive factors for 3�, we simply add 1 to the exponent:
7+1 = 8 positive factors.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
