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How many integers less than 100 have an odd number of factors?
There are 9 integers less than 100 that have an odd number of factors.Every factor of a number has a pair, eg 2 & 3 are a factor pair of 6; and so it would be expected that every number has an even number of factors.However, if the factor pair of a number are the same number (eg 6 & 6 are a factor pair of 36), then there will be an odd number of factors.When there is a repeated factor like this, the number is a perfect square.Thus only perfect squares have an odd number of factors.Less than 100 there are 9 perfect squares (1, 4, 9, 16, 25, 36, 49, 64 & 81) which have an odd number of factors.100 itself is a perfect square and also has an odd number of factors, but the question asked for those numbers less than 100 with an odd number of factors.
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.
What number has 6 factors pair?
60 has 6 factor pairs.
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 is the relationship between the rectangles for number and factors of the number?
One rectangle for each factor pair.
Is the greatest common factor of a pair of numbers always equal to or less?
Always equal to or less than the smaller number, yes.
How many integers less than 100 have an odd number of factors?
There are 9 integers less than 100 that have an odd number of factors.Every factor of a number has a pair, eg 2 & 3 are a factor pair of 6; and so it would be expected that every number has an even number of factors.However, if the factor pair of a number are the same number (eg 6 & 6 are a factor pair of 36), then there will be an odd number of factors.When there is a repeated factor like this, the number is a perfect square.Thus only perfect squares have an odd number of factors.Less than 100 there are 9 perfect squares (1, 4, 9, 16, 25, 36, 49, 64 & 81) which have an odd number of factors.100 itself is a perfect square and also has an odd number of factors, but the question asked for those numbers less than 100 with an odd number of factors.
What is a number less than 20 and has 3 factors?
4 and 9. Factors of numbers come in pairs which means that every number ought to have an even number of factors. To have an odd number of factors, one factor pair must be a repeated number which means that only square numbers have an odd number of factors. The square numbers less than 20 are 1, 4, 9 & 16 and of these 4 & 9 have 3 factors: 4: 1, 2 & 4 9: 1, 3 & 9
A number with only one pair of factors?
A number with only one factor pair is........ a prime number for example 11 the only factor pair is one times 11.
What are the factor and pair of the number 191?
191 is prime. It has one pair of factors, one and itself.
What kind of number has more than one pair of factors?
A composite number.
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.
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.
What number has 6 factors pair?
60 has 6 factor pairs.
What are all the pairs integers factors of 11?
There is only 1 pair of factors for the number 11.The pair is 1 & 11.This means that 11 is a prime number. It is only evenly divisible by 1 and itself.
What is a factor pair of 61?
Its factors are 1 and 61 because as a prime number it has only two factors
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.
