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Because if you think about it, a square number has two factors that are the same. For example, look at the number 16. Its factors are 1, 2, 4, 8, and 16. 1 and 16 go together, 2 and 8 go together, and then 4 gets paired up with another 4.
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How many factors do perfect square numbers have?
It depends what square number you're looking at. The square number 25 has only three factors (1, 5 and 25) but the square number 16 has 5 (1, 2, 4, 8 and 16.) A key point is that the factors don't pair up. There is always one middle factor that is the square root of the number and so cannot pair with any other factor. This means that all square numbers have an odd number of factors, while other numbers have an even number of factors.
What numbers have exactly 3 factors?
All numbers that are the square of primes have exactly 3 factors.
Is 25 a triangular number?
No - but it is a square number. 1,3,6,10,15,21 & 28 are all triangular numbers. 1,4,9,16,25 & 36 are all square numbers.
What is a perfect square factor?
All numbers have factors. Some factors are perfect squares. We call these perfect square factors. 9 is a perfect square factor of 27.
What are all the odd square numbers?
There are infinitely many of them. The square of every odd number will be an odd square number.
Which number has an odd number of different factors?
All square numbers have an odd number of factors.
Do all numbers have an even number of factors?
No. Perfect square numbers have an odd number of factors.
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.
What are two examples of a type of number that has an odd number factor?
There are square numbers (numbers which are a square of an integer), such as 4. It's factors, listed are 1, 2, and 4. All square numbers have an odd number of factors. Then there's 1, which has only 1 factor: 1. All other numbers have an even number of factors. Prime numbers will have only 2 factors (2 is even).
What is special about the number of factors for square numbers?
Square numbers have an odd number of factors, all others have an even number. In this context, primes can either be considered as having 0 factors (an even number) or 2 factors - 1 and itself, again, an even number.
What type of number has a n odd number of factors?
all perfect square numbers
Why do all numbers other than square numbers have an even number of factors?
Factors come in pairs. It is only in the case of a square number that the two middle factors are equal and so are counted only once.
What are the factors of a squared number?
Different square numbers have different sets of factors. The only thing they all have in common is an odd number of factors.
Explain why a prime number can't be a square number?
Prime numbers have two factors. All square numbers (other than 1) have more than that.
Are all square numbers also composite numbers explain?
Every square number (except 1) is composite. Prime numbers only have two factors, one and the numbers themselves. Since square numbers also have at least the square roots as factors, they have to be composite.
Do all square numbers have exactly 3 factors?
No. 81=9*9=3*27=1*81 81 has 5 factors and is a square number. 36=6*6=3*12=1*36=2*18=4*9 36 has 9 factors and is a square number. This doesn't mean that no square numbers have exactly 3 factors though, because: 9=3*3=1*9 9 has 3 factors and is a square number. 4=2*2=1*4 4 has 3 factors and is a square number. All square numbers have an odd number of factors though (because they have a whole number which multiplies by itself to get the number). Factors are whole numbers only, and not decimals. Hope this helps :)
Is 2500 a square number?
To find out if a number is a square number, find its prime factors and check if all prime factors duplicate. In this example, the prime factors are: 2,2,5,5,5,5 We can see that all numbers are duplicates, and can be paired up. So 2500 is a square number of 2x5x5 or 50.
