Not only can they, but they must.
An odd number cannot have an even factor. So none of the factors of either of the two odd numbers can be even and so the GCF is made up of only odd factors and so it must be odd.
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No. An odd number has no even factor. So two odd numbers can't have the same even factor.
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There is neither a greatest common factor nor common factors of a single number, such as 2060, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.
There is neither a greatest common factor nor common factors of a single number, such as 39, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.
The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! The greatest factor of any number is itself.
Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 1734, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.
There is neither a greatest common factor nor common factors of a single number, such as 3654, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.