Different square numbers have different sets of factors. The only thing they all have in common is an odd number of factors.
The prime factors of a squared number are the prime factors, if any, of its square root.
A prime number is a positive integer with two factors: one and the number itself. A squared number is any integer multiplied by itself. With the exception of 1, all squared numbers are composite.
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Okay, whoever said that a number can only have an even number of factors IS Wrong Take a prime number and square it. If you square a prime number, the number you get will only have 3 factors. For example, if I squared the number 3, I would get 9. 9 only has three factors: 9, 3, 1 Any prime number squared has Three factors.
No because then it will have more than two factors
This number would have to be a squared number as it only has 15 factors. The number I have calculated is 324 as the square root is 18
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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91 is neither a prime nor a squared number. It is a composite having the prime factors 7 x 13.
Any prime number to the 5th power squared has 11 factors, like 1024 or 59049.
No. That isn't possible: A prime number, by definition, has no smaller factors. A square number does have a smaller factor - the number that is squared.
9 squared is 81. Two digits lower than 81 is 79. 79 is a prime number. Its only factors are one and itself. That does not compute. 78 has 26 and 6 as factors. 78 is three digits lower than 81. That does not compute.