Page 183 - New Medley 4 Semester 1

Factors

There are 24 potted plants. A gardener is asked to keep them in rows so
that each row has the same number of pots. Can you guess how many
possibilities are there?

She can keep 24 pots in a single row or 12 pots in each of the two rows or
8 pots in each of 3 rows or 6 pots in each of the 4 rows. That means

1 × 24 or 2 × 12 or 3 × 8 or 4 × 6 = 24 pots

Here, we can say that all the numbers 1, 2, 3, 4, 6, 12 and 24 are the

factors of 24 as each of them exactly divides the number 24.

Thus, factors are the numbers which when multiplied give the product. In
other words, a factor is a number which divides the given number exactly.

Properties of Factors

Z Z 1 is a factor of every number. It is the smallest factor of a number.

Z Z Every number is a factor of itself. It is the greatest factor of a number.

Z Z A factor of a number is less than or equal to the given number.

Z Z 1 is the only number which has only one factor.
Z Z Every number other than 1 has at least two factors 1 and the number itself.

Z Z A number has limited factors.

Finding Factors of a Number

We can find the factors of a number by using two methods, multiplication

and division.

Multiplication Method

In this method, we try to find the numbers whose product is the given number.

Let us find the factors of 15.

1 × 15 = 15

2 × ? = 15 We cannot think of the number that can
3 × 5 = 15 give this product.

4 × ? = 15

\ 1, 3, 5 and 15 are the factors of 15.

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