Prime Numbers and Factorisation
Divisibility
Prime numbers: Rectangular numbers
Prime numbers: Factorisation
![Prime numbers: Rectangular numbers](https://static.studi.se/lessons/thumbs_small/MAH170.png)
Prime numbers: Rectangular numbers
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Which rectangle can you make from the number 8?
Leon is making cupcakes. He's making 30 of them. You can't arrange them like that. They have to be in neat rows. There's enough batter for one more cupcake.
No, this doesn't work. Five more will be okay, one more in each row. Or six more, one in each column. It has to be a rectangle. What are you talking about?
Rectangle? Look, there exist rectangular numbers. They can be divided into rows of equal length. Here are six magnets. Make a rectangle out of them.
Like this? Exactly, two times three it's a rectangle. You can do it the other way as well, three times two. Here are three more. What rectangle can you make with them?
Like this? Exactly, nine is three times three. This is a square number. Three squared is nine, but squares are also rectangles so it is a rectangular number as well. Hey, this is what they did when they made the American flag.
The U.S. consists of 50 states. On the flag there are stars in one corner, one for each state. For a long time there were only 48 states and the flag looked like this. 48.
A good rectangle number, six rows with eight stars in each. Six times eight is 48. Yes, but in 1959 Alaska and Hawaii also became states. They went from 48 states to 50 and had to increase the number of stars on the flag from 48 to 50. No problem, 50 can be a rectangle.
Five times ten for example. Sure, but how pretty is that? This is what they did instead. They divided 50 into two rectangles. One with 30 and one with 20 stars like this, and then like this.
Nice! This is how they made the inner, smaller rectangle. 20 is four times five, but there are more rectangles you can make from 20. Check this out. Two times ten is also a rectangle.
Okay, I can do this. No, that doesn't count. In that case, all numbers would be rectangular but they're not. Here, take 11 magnets and try it out. Okay, 11 is not a rectangular number.
No, it is not. It is a prime number. Prime numbers are such numbers that you can't make an even rectangle out of them. 31 is a prime number. So you can't put 31 cupcakes in a nice rectangle on a pan.
Mm, now it's only 30.