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.

_________________

~fluke

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