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Are multiples and divisors the same thing?
No.
Why are multiples and factors opposites?
Let's deny the premise. I don't think they are opposites. The opposite of a factor is a non-factor or a number that is not a factor and in special cases factors and multiples are the same. 10 is both a factor and a multiple of 10.
What is the difference between factor pairs and distinct factor pairs?
The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.
Why do all numbers other than square numbers have even factors?
All numbers can be broken down into factor pairs. No matter how many pairs there are, it's an even number of factors. Squares have a factor pair that consists of the same number twice. When you list them, you list the number once.
Is the number of factor pairs for a number equal to the number arrays for the same number?
Oh, what a lovely question! When we talk about factor pairs for a number, we're looking at pairs of numbers that multiply together to give us that number. Arrays, on the other hand, are rectangular arrangements of objects. While the number of factor pairs for a number may not always be the same as the number of arrays for that number, both concepts help us explore the beauty of numbers in different ways.
