**Multiples:**

- In mathematics, factors are those numbers which divide another number completely without leaving the remainder i.e. with zero remainder.
- Also, by multiplying the two or more factors we will get another number also, the number which we will get after multiplying the factors of the number is called as the multiple.

**For example:**

12 can be written as, 12 = 1*12

12 = 3*4

12 = 6*2

Thus, here 1, 2, 3, 4, 6 and 12 are the factors of 12.

While 12 is the multiple of 1, 2, 3, 4, 6 and 12.

Thus, the relationship between factors and multiple is given by,

Multiple = Factor* Factor

We see that, the numbers we get in the table of 2 are all the multiples of 2 because they are the results of multiplication of other numbers which is explained as follows.

**Properties of multiples:**

- We have to note that, factors are only positive or negative whole numbers not fractions.

Similarly, multiples are also the positive or negative whole numbers not fractions.

**For example:**

3*4 = 12, hence 3 and 4 are the factors of 12 and 12 is the multiple of 3 and 4 also.

But, 4*1/2= 2 is not possible, because ½ is the fraction here.

- The factors of any number are finite in number always, but the multiples of a number are infinite in number.

**For example:**

If we find the multiples of 4 which are 4, 8, 12, 16, 20, 24, 28, 32… and so on. Thus the multiples of a number are infinite in number.

- Factor of any number is less than that number or equal to that number always and the multiple of a number is greater than or equal to the number itself.

**For example:**

12 is the multiple 2, 3, 4, 6 and 12 itself. Here 12 is the multiple which is greater than 2, 3, 4 and 6, also equal to 12.

- Every number except 0 and 1, all has factors 1 and the number itself.

While every number is the multiple of itself.

**For example:**

12 can be written as 12 = 1*12

Hence, here 1 and 12 are the factors of 12.

So, 12 is the multiple of 1 and the number 12 itself.

**For example:**

- If we have to find the factors of 18.

Then, 18 = 6*3, 18 = 1*18

18= 2*3*3, 18 = 2*9

Thus, the factors of 18 are 1, 2, 3, 6, 9 and 18.

- And also, -1, -2, -3, -6, -9 and -18 all are the factors of 18.
- Because, when we take multiplication of two negative numbers then the answer will be positive.

Like, 18 = (-9)*(-2)

Hence, we can say that, 18 is the multiple of 1, 2, 3, 6, 9, 18, -1, -2, -3, -6, -9 and -18 also.