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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.
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Numbers that have an odd number of factors?
Square numbers have an odd number of factors.
Which number has an odd number of different factors?
All square numbers have an odd number of factors.
Odd number factors?
Perfect squares are numbers with an odd number of factors.
What factors are odd?
Square numbers have an odd number of factors, but beyond that, any odd number can be a factor.
Which nmbers beteen 50 and 60 have an odd number of factors?
Square numbers have an odd number of factors. There are no square numbers in that range.
Numbers that have an odd number of factors?
Square numbers have an odd number of factors.
Can an odd number have odd numbers of factors?
Yes. Square numbers have an odd number of factors. 49 has three factors.
Numbers with an odd number of factors?
Square numbers have an odd number of factors.
What middle numbers have an odd number of factors?
Square numbers have an odd number of factors.
What type of numbers has an odd number of factors?
Square numbers have an odd number of factors.
Odd number of factors?
Square numbers have an odd number of factors.
What numbers with an odd numbers of factors?
Perfect squares have an odd number of factors.
What type of number has odd numbers as factors?
Both odd and even numbers may have odd numbers as factors.
What kind of factors have an odd number of factors?
Square numbers have an odd number of factors.
Which number has an odd number of different factors?
All square numbers have an odd number of factors.
Which numbers between 50 and 60 have an odd number of factors?
No numbers in that range have an odd number of factors.
Can a number have an odd number of factors?
Yes, quare numbers have an odd number of factors.
