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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
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Answer is B.

thats the only integer which doesnt have an integer divisor>1 and also a square of other integer.
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
Acer86 wrote:
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?
(A) 75
(B) 42
(C) 32
(D) 25
(E) 12



I have no clue as to how to attempt this question. Can someone help me out :(

Converting the choices does the trick. Ans. B
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
Correct Answer B

All others have square whose integer is greater than 1
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
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Acer86 wrote:
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?

(A) 75
(B) 42
(C) 32
(D) 25
(E) 12


Since the factors of 42 are: 1, 2, 3, 6, 7, 21, and 42, we see that none of those factors are perfect squares greater than 1.

Answer: B
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
Acer86 wrote:
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?

(A) 75
(B) 42
(C) 32
(D) 25
(E) 12



We have to find a Divisor > 1. which is not = D^2

find the factors of all the options

Just browsing over the options, can make you realize B as the answer

2*3*7
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
right option will not have a factor that is perfect square of some other integer.

Prime factorisation:
A: 75 = 5*5*3 => having factor 25 that is a perfect square of 5
B: 42 = 7*3*2 => does not have any perfect square as a factor.
C: 32 = 2*2*2*2*2 => having factor 4 that is a perfect square of 2
D: 25 = 5*5 => having factor 25 that is a perfect square of 5
E: 12 = 2*2*3. => having factor 4 that is a perfect square of 2
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
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Acer86 wrote:
Which of the following integers does NOT have a divisor greater than 1 that is the square of an integer?

(A) 75
(B) 42
(C) 32
(D) 25
(E) 12


It is a factorisation problem. No perfect square in the divisors just means that when we prime factorise it, there will be no prime number with an exponent of 2 or more.

\(75 = 3 * 5^2\) (5 has an exponent of 2 hence 25 is a factor of 75)
\(42 = 6*7 = 2*3*7\) (No exponent of 2 or more)

Answer (B)

Check out this video on Factorisation: https://youtu.be/Kd-4cH4cqHw
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Re: Which of the following integers does NOT have a divisor greater than 1 [#permalink]
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