Q: Do all square numbers have a odd number factor?

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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).

yes because square numbers have to be hole numbers to be square

Suppose you have a number n which is not a square. Suppose now that a is a factor of n ie there is some integer b, such that a*b = n. Now since n is not a square, b is not the same as a. Thus for every factor a, there is another factor b ie the factors come in pairs. Therefore, there are an even number of factors.

No square number is a prime number, since it has the number you squared as a factor. There are several square numbers less than 100. Just calculate the squares of all numbers, starting with 1, until you reach or pass 100. Then stop.

Consider a number k. Let m be the square root of k : since k is not a square number, m is not an integer and so m cannot be a factor of k.Suppose p is a factor of k and suppose p< m.Then k has another factor q such that k = p*q and since p < m, then q> m.Thus, for every factor smaller than the square root, there is another factor that is larger than the square root. That is, the factors come is distinct pairs and so there is an even number of factors.

Related questions

The only square number in that range that has 32 as a factor is 64.

Yes, because each factor must have another factor to go with it, but the square root of a number can have itself as a pair.

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).

No. Any square number has an odd number of factors e.g. 25 = 1, 25, 5

yes because square numbers have to be hole numbers to be square

Suppose you have a number n which is not a square. Suppose now that a is a factor of n ie there is some integer b, such that a*b = n. Now since n is not a square, b is not the same as a. Thus for every factor a, there is another factor b ie the factors come in pairs. Therefore, there are an even number of factors.

A number with a square root is still a number. So the answer is all of them.

All square numbers have an odd number of factors.

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.

No square number is a prime number, since it has the number you squared as a factor. There are several square numbers less than 100. Just calculate the squares of all numbers, starting with 1, until you reach or pass 100. Then stop.

Possiblilty is almost 1/2 cause every two numbers is a number with a factor of 2.From 2: 2,3,4,5,6,7,8,9,10...

Only the number 1 is a factor of all other integers.