Which of the following integers does NOT have a divisor greater than 1

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
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Prime factorization
75 = 5*5*3 = 5^2*3. Includes a perfect square 25
42 = 7*6 = 7*3*2. We got our candidate. No perfect squares here.
32 = 2^5 = 4^2*2. Includes a perfect square 4
25 = 5^2. Perfect square 25
12 = 2^2*3 = Perfect square 4.

All but 42 have perfect square in them as a factor.
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Just write down all perfect squares greater than 1 and less than 75;
4,9,16,25,36,49,64

75 = 25*3. 25 is a perfect square
42 = 7*2*3. No perfect squares here
32 = 16*2. 16 is a perfect square
25. 25 is a perfect square
12 = 4*3. 4 is a perfect square

Ans: "B"
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I guess this is also somewhere else in the forum.

The answer is B, all other choices have square of an integer > 1 as a factor.
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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.

Converting the choices does the trick. Ans. B

Correct Answer B

All others have square whose integer is greater than 1

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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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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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

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