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What is a number called that has an odd number of factor pairs?
A square number has an odd number of factors, but a number with an odd number of factor pairs is nothing special.
Why do all non square numbers have even factors?
The factors of all numbers can be written in pairs. With square numbers, one of those pairs is the same number twice. When listed singly, square numbers have an odd number of factors. All others are even.
Why does a square number always have an odd number of factors?
Factors can be listed as factor pairs. With square numbers, one of those pairs will be the same number twice. When written as a list, only one of them will be used, leaving 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.
What is the meaning of even and odd factors?
All nonzero numbers have factors. Some factors are even numbers, some factors are odd numbers.
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.
Is the number of factors of any square number odd or even?
Odd.
What 7 odd numbers that will total 30?
You cannot do this, because you're taking odd numbers: if you add two odd numbers together, you will get an even number. Take the odd numbers in pairs, so you'll have 3 pairs plus an extra odd number. The 3 pairs make 3 even numbers. You can add up any number of even numbers and get an even number, so you will have an even + odd, which is odd. 30 is an even number, but your result will be odd, no matter what 7 odd numbers you choose.
Numbers that have an odd number of factors are?
Perfect squares ( also called square numbers) have an odd number of factors and primes squared have 3 factors. Brief Explanation: If you start with a prime number, it has 2 factors by definition. Square that number and you have 3 factors, which is an odd number. So primes squared always have an odd number of factors. For example, 5 has 1 and 5 as factors, 25 has 1,5, and 25. What about an odd number such as 21 which is not the square of a prime. It has factors 1, 21, 3 and 7 so an even number of factors. How about 27, 1,27, 3, 9 once again even. What I was trying to show is that factors of numbers come in pairs and so only certain numbers will have an odd number of factors. Let's look at one more perfect square that is not a prime squared. How about 16 which is 4 squared. The factors are 1,2,4,8,and 16 which is an odd number of factors. Looking at these as pairs we see the factor pairs of 16 are 1 x 16, 2 x 8, and 4 x 4, giving us the factors of 1, 2, 4, 8, and 16 - an odd number of factors. So we conclude that perfect squares have an odd number of factors and primes squared have 3 factors.
Does a prime number have an even or odd number of factors?
Even
Do odd numbers have a odd or even number of factors?
The number of factors can be either even or odd.
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.
