a square number
A factor rainbow will show all of the factors. A factor pair is just 2 numbers that are factors of the number you want to find.
A square number
One factor pair of square numbers would be the same number twice. When you list them, you only write it once.
It's a square number. Square numbers have a factor pair that is the same number twice. When listed, that number occurs once.
A number pair whose GCF is the same as one of the numbers is i , i x j where i and j are integers greater than zero. If i=3 and j=5 then the number pair will be 3,15. The GCF is 3. If i=7 and j=11 the number pair will be 7,77 and the GCF 7. The number of possible solutions is infinite.
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.
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.
Only if the magnitudes of two numbers are the same.
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.
There are at least nine different factor trees for 2000, one for each of its non-trivial factor pairs. Eighteen, if you consider the reverse of each pair to be a separate pair. The important information to remember is that it doesn't matter what factor pair you choose to start the tree. But since, if done correctly, all the factor trees will have the same number of branches and arrive at the same factors for the bottom branch, it's a waste of time to write them all out. 2000 1000,2 500,2,2 250,2,2,2 125,2,2,2,2 25,5,2,2,2,2 5,5,5,2,2,2,2 2000 50,40 25,2,40 5,5,2,40 5,5,2,20,2 5,5,2,10,2,2 5,5,2,5,2,2,2
No.
C2h4, c3h6, c4h8