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.
The number 64 has an odd number of factors because it is a perfect square of 2 raised to the power of 6. When a number is a perfect square, it has an odd number of factors because each factor has a corresponding pair, except for the square root itself. In this case, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64, totaling 7 factors, which is an odd number.
Factors of the number 6 are 1,2,3,6
A factor pair is two numbers. A factor pair is the set of two factors that when multiplied together result in the number of which they are factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factor pairs are 1 x 12, 2 x 6, and 3 x 4.
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.
yesThe factors 10 and 6 are a factor pair of 60.
10, which has the factors 1,2,5 and 10. If the trivial pair 1 and the number itself are disallowed, the answer is 12 with factors 2,3,4 and 6.
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.
Divide a number by a factor, the result is another factor. These can be written in pairs. The factor pairs for 24 are (24,1)(12,2)(8,3)(6,4)
6 and 4
They are 4 and 6
A number with only one factor pair is........ a prime number for example 11 the only factor pair is one times 11.
Most numbers have more than one factor. I'm guessing you're asking about common factors. Consider 6 and 9. The factors of 6 are 1, 2, 3, 6 The factors of 9 are 1, 3, 9 The common factors of 6 and 9 are 1 and 3.
191 is prime. It has one pair of factors, one and itself.
A composite number.
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288 2 and 3 are prime.
60 is a composite number, that has twelve factors. They are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. ... Pair Factors of 60. Positive Factors of 60 Positive Pair Factors of 60 4 × 15 (4, 15) 5 × 12 (5, 12) 6 × 10 (6,10)