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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.

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Q: Why 81 have an odd number of factors and 40 have an even number of factors?
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Related questions

Is 40 an odd number?

No, 40 is an even number.


Is 40 odd or even?

40 is an even number - it is divisible by 2 to produce a whole number


Which numbers between 1 and 40 have an odd number of factors?

These numbers between 1 and 40 have an odd number of factors: 4, 9, 16, 25, 36.


Is 20 and 40 an even or odd number?

they are even


Which number between 30 and 40 has an odd number of factors?

That number is 36.


What odd number is less than 40 and has exactly three prime factors?

27


How many odd numbers are between 20 and 100?

There are 40 odd numbers between 20 and 100. Remember that an odd number is every second number. There are 80 numbers between 20 and 100, so there are 40 odd numbers and 40 even numbers.


What number between 12 and 40 have 3 factors?

only 2516 and 36 also have an odd number of factors, but both of those have more than 3.


Is 40 odd number?

No.


What is a number between 12 and 40 that has three factors?

Square numbers have an odd number of factors. Other numbers have an even number of factors. The squares between 12 and 40 include 16, 25, and 36. If the number has only three factors, it must be the square of a prime number, since two of the factors will be 1 and itself, so if there is only one more factor, this third number cannot have factors itself. This means the number must be 25, whose factors are 1, 5, and 25. Response: 24 has (at least) three factors - 1, 2, 3, 4, 6, 8, 12, and 24 .


What odd number is between 21 and 40 with a odd sum of 8?

There can be no number with an odd sum of 8 because 8 is not odd!


Is 40 odd or even why?

Even because it is divisible by 2.