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What is the meaning of even and odd factors?
All nonzero numbers have factors. Some factors are even numbers, some factors are odd numbers.
What type of number has odd numbers as factors?
Both odd and even numbers may have odd numbers as factors.
What types of numbers has an odd number of factors?
Even powers of prime numbers. Square numbers have an odd number of factors.
What is a number has an odd number of factors?
An even power. Square numbers have an odd number of factors.
How are odd and even numbers are related to their factors?
Even numbers must have 2 amongst their factors; they may have other even numbers amongst their factors. Odd numbers must not; every factor of an odd number must be odd.
Do all numbers have an even number of factors?
No. Perfect square numbers have an odd number of factors.
Does composite numbers have an odd number of factors?
Composite numbers can have either an odd number or an even number of fractions. Factors of 25 are 1, 5, 25 . (odd number of them) Factors of 26 are 1, 2, 13, and 26 . (even number of them)
Can the GCF of an odd number and an even number ever be even?
No. Odd numbers don't have even factors.
Does every number have an even number of factors?
No, square numbers have an odd number of factors.
Do only square numbers have an even number of factors?
No, only square numbers have an odd number of factors.
Are the factors of an odd number always odd?
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.
Is the greatest common factor of any 2 odd numbers odd?
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.
