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Is the greatest common factor of an odd and even number always 1?
No, the GCF of an odd an even number is not always 1. Odd and even numbers can share factors other than 1. For example, the greatest common factor of 5 and 10 is 5.
Why do all numbers other than square numbers have even factors?
All numbers can be broken down into factor pairs. No matter how many pairs there are, it's an even number of factors. Squares have a factor pair that consists of the same number twice. When you list them, you list the number once.
Is the greatest common factor of two numbers is equal to the lesser of the number?
Well, not always. The GCF and LCM of 10 and 10 is 10. But apart from that special circumstance, the statement is true. Apart from a number itself, all of its factors are smaller than it. Apart from a number itself, all of its multiples are larger than it. You can't have a GCF that is greater than the smaller number, and you can't have an LCM that is less than the larger one which means that the LCM of two numbers will never be less than the GCF. Factors go into numbers, numbers go into multiples.
What number less than 13 has the most factors?
1 is the number less than fifty with the fewest number of factors. All other numbers have at least two factors (1, and the integer itself).
Is a factor a multiple?
As a general rule, multiples tend to be larger than factors. This is not always true. 9 is a factor of 27. 6 is a multiple of 3. The important distinction is in the relationship to the number they are factors or multiples of. A factor will be equal to or lesser than the number. A multiple will be equal to or greater than the number.
