Q: What type of number has odd numbers as factors?

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No numbers in that range have an odd number of factors.

There are 31 numbers less than 1,000 which have an odd number of factors. They are: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961.

Only if an odd number of the factors are negative numbers.

Yes. An even number is defined as being evenly divisible by 2 (no fractional answers, only integers). If an odd number has an even factor, then because of the above definition, this odd number must have a factor of 2. But you will be hard pressed to find an odd number that is a multiple of 2, because that is already the definition of an even number. So, odd numbers cannot have even factors and thus odd numbers always have odd factors.

There are 12 numbers less than 150 which have an odd number of factors: 1,4,9,16,25,36,49,64,81,100,121,144.

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Square numbers have odd numbers of factors. Examples: 4, 9, 16

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