GRE® Quant Practice Q7

This GRE maths sample question is a Select One or More Answers question in Number Properties. Concept tested: Number of factors of a number.

Question 7: Which of the following numbers has an even number of positive integer factors? Indicate all such numbers?

1. 29
2. 116
3. 216
4. 384
5. 676
6. 576

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Video Explanation

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Explanatory Answer | GRE Problem Solving Question 7

Concept: What kind of numbers have even nuber of factors?

All perfect squares have odd number of factors.
Any other number will have an even number of factors.
We are looking for options in which the number given is not a perfect squares.

Choice A: 29
29 is not a perfect square.
The factors of 29 are 29 and 1.
29 has even number of factors and hence, is a correct answer.

Choice B: 116
116 is not a perfect square.
The factors of 116 are 1, 2, 4, 29, 58, 116.
116 has even number of factors and hence, is a correct answer.

Choice C: 216
216 is not a perfect square.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.
216 has even number of factors and hence, is a correct answer.

Choice D: 384
384 is not a perfect square.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384.
384 has even number of factors and hence, is a correct answer.

Choice E: 676
676 is a perfect square.
The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
The value of 26² is 676.
676 has odd number of factors and hence, is not a correct answer.

Choice F: 576
576 is a perfect square.
The factors of 576 are 1,2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96,144, 192, 288, and 576.
The value of 24² is 576.
576 has odd number of factors and hence, is not a correct answer.

Choices A, B, C, D are the correct answers.