hja379 wrote:2600 has how many positive divisors?
OA
24
To determine the number of positive factors of an integer:
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
Since 2600^2 = 2³ * 5² * 13¹, we get (3+1)*(2+1)*(1+1) = 24 factors.
The correct answer is
D.
Here's the reasoning. To determine how many factors can be created from 2600^2 = 2³ * 5² * 13¹, 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 5, we can use 3�, 3¹, or 3², giving us 3 choices.
For 13, we can use 13� or 13¹, giving us 2 choices.
Multiplying our number of choices for each factor, we get 4*3*2 = 24 possible factors.
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