Prime Numbers

Guna and Anshu want to pack figs (anjeer) that grow in their farm. Guna wants to put 12 figs in each box and Anshu wants to put 7 figs in each box.

How many arrangements are possible?

Think and find out the different ways how—

1. Guna can arrange 12 figs in a rectangular manner.
2. Anshu can arrange 7 figs in a rectangular manner.

Guna has listed out these possibilities.

Observe the number of rows and columns in each of the arrangements. How are they related to 12?

In the second arrangement, for example, 12 figs are arranged in two columns of 6 each or 12 = 2 × .

Anshu could make only one arrangement: 7 × 1 or 1 × 7. There are no other rectangular arrangements possible.

In each of Guna's arrangements, multiplying the number of rows by the number of columns gives the number 12. So, the number of rows or columns are of 12.

We saw that the number 12 can be arranged in a rectangle in more than one way as 12 has more than factors. The number 7 can be arranged in only one way, as it has only factors a .

What about numbers that have more than two factors? They are called compositeprime numbers. The first few composite numbers are—4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

What about 1, which has only one factor?

The number 1 is neither a nor a number.