At the elementary level, factors and multiples are introduced. Factors are numbers that split a given number precisely, whereas multiples are numbers that multiply a given number. Let's understand them closely.

Factors of a number

Both factors and multiples of a number may seem similar as they involve multiplication. To elaborate, factors of a number are nothing but certain sets of numbers which when multiplied offer a number. For example, we can get a number six, when we multiply one and six or two and three. 

In numbers, it can be represented as:

6 = 1 x 6

Or

6  = 2 x 3

Thus here, we clearly see that when numbers one and six are multiplied, we get the number six. 

Similarly, when numbers two and three are multiplied, we get the number six.

Thus we can say that the factors of the number six are: one, six, and two, three.

Representing the factors of the number 6 = 1,2,3.

Let us move on to the concept of multiples.

Multiples of a number:

Multiples of the numbers in the form of integers, not fractions. We obtain them by multiplying a certain set of numbers with an integer.

Let us consider an example.

0 x 5 = 0

1 x 5 = 5

2 x 5 = 10

3 x 5 = 15

4 x 5 = 20 ……. and so on.

Here you look carefully, the numbers zero, 5, 10, 15, and various numbers can be divided by the integer five.

Thus, these numbers are multiples of five. Another interesting thing you will notice is that all these multiples are nothing but the different product numbers that can be divided by five. This is actually the table of five if you look at it carefully. Isn’t it easy!

Let us take another example. This will help you to gain a better understanding of the multiples of a number

0 x 2 = 0

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

4 x 2 = 8……. and so on.

Here you look carefully, the numbers zero, two, four, six, eight and various numbers can be divided by the integer two.

Thus, these numbers are multiples of two. 

You must have noticed that all these multiples are nothing but the different product numbers that can be divided by two. This is actually the table of two.

Can we have multiples of an integer in the form of negative numbers?

Yes, having multiples of an integer in the form of negative numbers is very much possible. Let us take an example to understand this concept.

We already know that the multiples of five are 0, 5, 10, 15,….

The above multiples lie on the positive side or on the right side of the zero on the number line.

But have you ever wondered what would happen if we moved to the left side of the zero on the number line?

Let us represent this in terms of numbers.

0 x 5 = 0

-1 x 5 = -5

-2 x 5 = -10

-3 x 5 = -15

-4 x 5 = -20 ……. and so on.

Here you would notice that the multiples of five are  0, -5, -10, -15, and so on.