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Is the GCF of any two numbers always odd and why?
The GCF of any two odd numbers is always odd because odd numbers don't have any even factors. The GCF of any two even numbers is always even because even numbers are divisible by two and any common factors would have at least one two in common. The GCF of an even and an odd number is odd because odd numbers don't have any even factors.
Do odd numbers always have an odd number of factors?
No. Consider 15: 1,3,5,15 Every positive whole number has an even number of factors, unless the number is a perfect square.
Do all numbers have an even number of factors?
No. Perfect square numbers have an odd number of factors.
Is even number times even number always even?
Yes, it is. Any whole number times an even number will be even. This is because whole numbers can be represented as the product of their prime factors. Every even number contains 2 as a prime factor (thereby excluding all even numbers above 2 from being prime.) Additionally, the product of any two numbers is equal to the product of their prime factors. This means that the result of multiplying an even number by a whole number will always have a prime factor of 2, making it an even number.
Does every number have an even number of factors?
No, square numbers have an odd number of factors.
