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What type of number has a odd number of factors?
A square number, because its square root is paired with itself.
Why 81 have an odd number of factors and 40 have an even number of factors?
A number will have an odd number of factors if and only if one of those factors is the square root of the number. This is because any factor of a number you can find must pair up with another factor of that number, and multiply to give the number. The only exception is when the factor would be paired with itself. In other words, be the square root. 81 is a square number, and so the factor 9 (square root of 81) will not pair with any other factor, meaning 81 will have an odd number of factors. 40 has an even number of factors, because it is not a square number, and so all its factors can pair up.
Why does a square number have an odd number of factors?
A square number will have one factor pair that consists of the same number (the square root). In the list of factors, that number will be written once.
What type of number has an odd number of factors?
A perfect square has an odd number of factors. Factors of numbers always come in pairs -- except for perfect squares. Since the square root of a perfect square is listed only once on the list of factors, it results in a list with an odd number of factors.
Why does number 25 have a odd number of factors?
Because it's a square number. All perfect squares have an odd number of factors because they have one factor pair that is the same number twice (the square root) and when the factors are listed, the number is listed once.
