How many factors does 36^2 have?
A. 2
B. 8
C. 24
D. 25
E. 26
The OA is the option D.
How can I solve this question is a fast way? Can anyone give me a good explanation? Thanks.
How many factors does 36^2 have?
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-------ASIDE-------------------VJesus12 wrote:How many factors does 36^2 have?
A. 2
B. 8
C. 24
D. 25
E. 26
The OA is the option D.
How can I solve this question is a fast way? Can anyone give me a good explanation? Thanks.
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
---NOW ONTO THE QUESTION-----------------
36 = (2)(2)(3)(3)
So, 36² = (36)(36)
= (2)(2)(3)(3)(2)(2)(3)(3)
= (2^4)(3^4)
So, the number of positive divisors of 36² = (4+1)(4+1)
= (5)(5)
= 25
Answer: D
Cheers,
Brent
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The approach here is to first find the prime factors of 36^2, and then add 1 to each prime factor's exponent and then find the product of those enhanced exponents. Thus, we have:VJesus12 wrote:How many factors does 36^2 have?
A. 2
B. 8
C. 24
D. 25
E. 26
36^2 = (6^2)^2 = (2 x 3)^4 = 2^4 x 3^4
The total number of factors of 36^2 is (4 + 1)(4 + 1) = 5 x 5 = 25.
Answer: D
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