(10000,1)(5000,2)(2500,4)(2000,5)(1250,8)(1000,10)(625,16)(500,20)(400,25)(250,40)(200,50)(125,80)(100,100)
The prime factors of 42 are 2, 3 and 7. I'd have to see the rectangles to know what to write in them.
Three factors whose product is about 10000 are 25, 20, and 20. This is because 25 x 20 x 20 = 10000. Another set of factors could be 50, 10, and 20, as 50 x 10 x 20 also equals 10000. In general, factors that are close to the cube root of 10000 (which is approximately 21.54) will have a product close to 10000.
The prime factors of 10,000 are: 2,5
24
22 is a composite number with four factors, which means two rectangles.
As I understand it, the number of factor pairs is equal to the number of rectangles.
If you can compile a complete list of all different rectangular models with sides of integer length for a number then their lengths and breadths represent its factors.
80
They are 16 and 625.
Some people like to visualize factors as representing the lengths of sides of rectangles. In the same way that length times width equals area, factor times factor equals product.
The number of rectangles you can build with a prime number of tiles depends on many factors such as shape, size, and uniformity of the tiles.
As a product of its prime factors in exponents: 24*54 = 10,000