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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.

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.

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.

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

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Yes. Square numbers have an odd number of factors. 49 has three factors.

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