195465

Xavi's T-shirt
I noticed that the circles that are all one colour, and not split up represent prime numbers. The top row shows the numbers 1-10, and the colours represent what lowest factors multiply to make them. For example, the number 10 has two colours: pink, which represents the number 2, and yellow which represents the number 5. 2 X 5 = 10.
What's special about the fifth column is they all end in a 5, and all have 5 as one of their factors. This is every other multiple of 5, so all the multiples that don't divide by ten to get an integer. These also show the factors. The farthest column to the right shows the number 10's multiples to 100. All of the numbers that have pink and green divide by 6, because pink=2 and green=3, and any number that has a factor of 2 and 3 must be a multiple of 6.The reason why the 11 and 9 times tables are on a diagonal line is because it is a hundred square, meaning 10 rows and 10 columns, 9 and 11 are both one away from 10, so each one will be one place ahead or behind the last. The only other number that will have 3 segments, each the same colour is 27, because it is its lowest common factor (3) cubed (which is why there were three segments).
I spotted that this is a hundred square based on prime numbers and factors, usually lowest common factors.
Looking at this challenge made me think, for I'd never seen anything like it before! It was full of strange circles and different colours that left me puzzled for a while. Xavi's T-shirt is a 2-step problem, so you have to figure out what each circle means before you can even consider most of the questions. To solve the questions, I had to imagine each what each one meant, and only figured it out as there was no 1, because 1 is neither prime nor composite.