Prime numbers

In your book, Maths Mela (Chapter 13, Animal Jumps), you make arrays for 10, 14, 13, 20, 25, 32, 37, 46 and 54. Most of these can be made in more than one way. 14 can be 2 rows of 7. 25 can be 5 rows of 5. 54 can be 6 rows of 9.

But try 13 squares. 2 rows? 2 × 6 = 12 and 2 × 7 = 14, so no. 3 rows? 3 × 4 = 12 and 3 × 5 = 15, so no. However you try, 13 squares will only go in one single row: 1 × 13. The same happens with 37. So the only factors of 13 are 1 and 13, and the only factors of 37 are 1 and 37.

The book says numbers like 13 and 37 are called prime numbers. Why? Because a prime number has only two factors: 1 and the number itself. Its only array is a single row.

A number that can be made in another way is not prime. 20 is not prime, because 20 = 4 × 5, so 4 and 5 are factors too. (The number 1 is not called prime either: it has only one factor, 1 itself.)