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.
