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How do you find whether a number is a perfect square by using its prime factors?
In the prime factorisation of the number, each factor must appear an even number of times.In the prime factorisation of the number, each factor must appear an even number of times.In the prime factorisation of the number, each factor must appear an even number of times.In the prime factorisation of the number, each factor must appear an even number of times.
How are odd and even products related to their factors?
2 cannot be a factor of an odd number, 2 must be a factor of an even number.
When you factor a number into its primes 2 is a factor then you know that the last digit must be what?
Even.
Is the greatest common factor of two even numbers always even?
Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater. Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.
What is a factor of 86?
It's an even number so 2 must be a factor. Try dividing 86 by 2...
Can two odd numbers have a greatest common factor that is an even number?
No. Because both numbers are even, they each have 2 as a factor. Even if they have a larger factor in common, it will be a multiple of 2, so the greatest common factor will be an even number.Yes. Two even numbers are each divisible by 2. The GCF must therefore always have two as one of its factors; this makes it even.
What number has an even factor?
Any even number has at least one even factor.
Is it true that the gcf of an odd and an even number is always an odd number?
Yes. The odd number does not have 2 as a factor (or else the number would be even). So the gcf does not have 2 as a factor. So the gcf must be odd.
Why is the product of two even numbers even?
An even number is any number that has '2' as a factor.When you multiply two numbers, you multiply all the factors of both of them.If '2' was a factor of either number, or of both, then it's a factor of their product,and the product must therefore be an even number.
Can the greatest common factor of an odd and even number always even?
The GCF of an odd and an even number must be odd since odd numbers do not have any even factors.
Is the gcf of an odd and even number always even?
No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.
How is 42 prime or composite?
It's an even number so 2 must be a factor so it is composite.
