To determine the number of positive factors of an integer:shikh wrote:How many factors does 36^2 have?
a.2
b.8
c.24
d.25
e.26
OA:D[spoiler][/spoiler]
1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply
36² = 2^4 * 3^4.
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 = 2^4 * 3^4, we need to determine the number of choices we have of each prime factor:
For 2, we can use 2^0, 2^1, 2², 2³, or 2^4, giving us 5 choices.
For 3, we can use 3^0, 3^1, 3², 3³, or 3^4, giving us 5 choices.
To combine the number of choices we have of each prime factor, we multiply:
5*5 = 25 factors.
