Prime or composite?

Guna and Anshu pack figs (anjeer) from their farm into boxes. Guna puts 12 figs in each box and Anshu puts 7. Each wants to arrange the figs in a rectangle.

Guna finds several ways: 1 row of 12, 2 rows of 6, or 3 rows of 4 (and the same rectangles turned round). In each one, rows × columns = 12, so the numbers of rows and columns are factors of 12. Anshu can make only one arrangement: 1 × 7, a single line. 7 has only two factors, 1 and 7.

Numbers that have exactly two factors, 1 and the number itself, are called prime numbers, or primes. The first few are 2, 3, 5, 7, 11, 13, 17, 19. Numbers with more than two factors are called composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 are the first few. For example, 4 has three factors (1, 2 and 4), so it is composite.

What about 1? It has only one factor, itself. So 1 is neither prime nor composite.

2 is a prime, and it is even. Is there any other even prime? No: every other even number has 2 as a factor as well as 1 and itself, so it has more than two factors. 2 is the only even prime. This also means not all even numbers are composite. Every prime after 2 is odd, but an odd number need not be prime: 15 = 3 × 5.