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.
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Yes, every factor pair in an array will have an equal pair, as factors are defined such that when multiplied together, they produce the original number. For example, if ( a ) and ( b ) are factors of a number ( n ), then ( a \times b = n ). In an array, each factor ( a ) will have a corresponding factor ( b ) such that both pairs are equal in their product, ensuring balance within the factor pairs. However, the arrangement of these pairs may differ depending on the context of the array.
One pair: it's a prime number.
The number of numbers in the string; how long it is.
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.
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The Number of factors, (That is the number of pairs, such as 2= 1x2, 2x1), is equal to the number of rectangular arrays which can be made for each composite number. As such, the number of factors in the number 9 is 3, (1,3,9), and the number of rectangular arrays is also three (1x9, 9x1,3x3). Hope this helps!
As I understand it, the number of factor pairs is equal to the number of rectangles.
its a factor with two pairs of the same number
These are the 16 factor pairs for the number 1,080:1080,1540,2360,3270,4216,5180,6135,8120,9108,1090,1272,1560,1854,2045,2440,2736,30
A square number has an odd number of factors, but a number with an odd number of factor pairs is nothing special.
Number of factor pairs = number of rectangles
The number 18.
12 and 18 have three factor pairs.
76 has 3 factor pairs: (1,76), (2,38), (4,19).
The factor pairs of 16 are (16,1)(8,2)(4,4)
12 and 18 have three factor pairs.