True or False?

All whole numbers other than 1 have an even number of positive factors.

True False

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4 solutions

Xiaoying Qin
Nov 12, 2015

Square numbers like 9, 16, 4, and 25 have odd square roots: 9- 1,3,9 16-1,2,4,8,16 4- 1,2,4, and 25- 1, 5, 25

I think you mean square numbers instead of square roots.

Raj Magesh - 5 years, 7 months ago

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Thank you. I have edited.

Xiaoying Qin - 5 years, 7 months ago

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You haven't edited

Kushagra Sahni - 5 years, 7 months ago

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@Kushagra Sahni Lol. Stupid submit button.

Xiaoying Qin - 5 years, 7 months ago
Edwin Gray
Sep 19, 2018

Let n = 4. Ed Gray

Joel Yip
Mar 18, 2016

To prove something is true in mathematics, every single values in the range must be true otherwise it is false.

Because the range is all whole numbers above 2 2 , we can start with that number.

2 2 has factors 1 1 and 2 2 so it has two factors.

3 3 has factors 1 1 and 3 3 so it has two factors.

However, 4 4 has factors 1 1 , 2 2 and 4 4 so it has three factors.

Since the condition is all numbers within the range having even number of positive factors, 4 4 does not satisty that, so False.

Plusle Atreides
Nov 15, 2015

The numbers {0, 1, 2, 3, ...} etc. There is no fractional or decimal part. And no negatives. Reference : http://www.mathsisfun.com/definitions/whole-number.html

Square numbers have twin factor other than itself and 1. So, the answer is FALSE

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