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The number of positive divisors
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18 Jun 2021, 01:22
18 Jun 2021, 01:22
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Quantity A |
Quantity B |
The number of positive divisors of 144 |
The number of positive divisors of 108 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The number of positive divisors
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18 Jun 2021, 07:31
18 Jun 2021, 07:31
1
Carcass wrote:
Quantity A |
Quantity B |
The number of positive divisors of 144 |
The number of positive divisors of 108 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
If \(N = (a^x)(b^y)(c^z)....\)
Where a, b, and c are its prime factors with powers x, y, and z
Then, total number of positive divisors is given by (x+1)(y+1)(z+1)....
Col. A: \(144 = (36)(4)\)
Col. B: \(108 = (36)(3)\)
Dividing both sides by 36;
Col. A: \(4 = 2^2\)
Col. B: \(3\)
Col. A: Divisors of \(2^2 = (2+1) = 3\)
Col. B: Divisors of \(3^1 = (1+1) = 2\)
Hence, option A
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The number of positive divisors
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18 Jun 2021, 11:09
18 Jun 2021, 11:09
2
Finding Factors(Divisors) of a Number
To find the factors of a number we need to follow following steps
- Do prime factorization of the number
- Add one to the power of all the powers
- Multiply them to get the number of factors
Quantity A: The number of positive divisors of 144
144 = \(2^4 * 3^2\)
=> Number of factors of 144 = (4+1) * (2+1) [ add one to the power 4 and 2 and multiply them]
= 5*3 = 15
Quantity B: The number of positive divisors of 108
108 = \(2^2 * 3^3\)
=> Number of factors of 108 = (2+1) * (3+1) [ add one to the power 2 and 3 and multiply them]
= 3*4 = 12
Clearly, Quantity A(15) > Quantity B (12)
So, answer will be A
Hope it helps!
To find the factors of a number we need to follow following steps
- Do prime factorization of the number
- Add one to the power of all the powers
- Multiply them to get the number of factors
Quantity A: The number of positive divisors of 144
144 = \(2^4 * 3^2\)
=> Number of factors of 144 = (4+1) * (2+1) [ add one to the power 4 and 2 and multiply them]
= 5*3 = 15
Quantity B: The number of positive divisors of 108
108 = \(2^2 * 3^3\)
=> Number of factors of 108 = (2+1) * (3+1) [ add one to the power 2 and 3 and multiply them]
= 3*4 = 12
Clearly, Quantity A(15) > Quantity B (12)
So, answer will be A
Hope it helps!
