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# 1) Factors of any odd integer will always be ODD. (2)

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Senior Manager
Joined: 20 Feb 2007
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1) Factors of any odd integer will always be ODD. (2) [#permalink]

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19 Mar 2007, 17:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

(1) Factors of any odd integer will always be ODD.

(2) Factors of any even integer can be even, odd or both.

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Senior Manager
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19 Mar 2007, 18:21
Summer3 wrote:
(1) Factors of any odd integer will always be ODD.

(2) Factors of any even integer can be even, odd or both.

Umm....

(1) If one of the factors of an odd integer is 2, then it would mean that the integer is divisible by 2, which means that the number is even. So I think it's TRUE.

(2) TRUE. Consider 6. It has both even (2,6) and odd (1,3) factors.
Hmm..this might be FALSE if it means that it can be ALL even. Cuz any number (whether even or odd) has an odd number 1 as one of its factors...

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20 Mar 2007, 17:54
rico makes an interesting point with the second statement...

but for the first statement:

even times an even will be an EVEN... 2x2

even times an odd will be EVEN... 2x3

odd times odd will be ODD... 3x3

so if you multiply a number (whether odd or even) by an even, you'll get an even... therefore, the only way to get an odd product would be to only multiply odd numbers

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20 Mar 2007, 17:54
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# 1) Factors of any odd integer will always be ODD. (2)

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