Multiples and Factors

This topic would deal with multiples and factors. There is one common element between the both that is both involve multiplication. We multiply the factors to get a particular number and multiples are the product that we get after multiplying a given number by the integer.


Definition of Multiple and Factors:

Multiple: Multiple is such a number that is divided by another number a few number of times without leaving a remainder.

For Example: 12 is the multiple of 3. As 12 can be divided by 3 without leaving behind remainder 4 times.

Factor: Factors are two or more numbers that divides other number without leaving behind a remainder.

For Example: 3 is the factor of 9 as 3 can completely divide 9 without leaving behind any remainder. Hence we can say that 3 the divisor is the factor of the dividend 9. The common factor of every number is 1 and the number itself.

More Examples:

The factors of 12 are: 1, 2, 3, 4, 6, 12

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …..

5 is a factor of 60 because 5 can exactly divide 60 without leaving behind any remainder and the quotient is 12. Hence, 12 is also the factor of 60 giving a quotient 5. Hence we can say that 5 and 12 both are factors of 60 in addition to other factors like 1, 2, 3, 4, 6, 10, 15, 20, 30, and 60. Again from this list of factors of 60 we get to know that 2 is a factor of 60 as 2 completely divides 60 by giving 30 without leaving any remainder. Alternatively, the quotient 30 is also a factor as it divides 60 by giving 2 without leaving any remainder.

Some numbers have only two factors that is 1 and the number itself. Such numbers are called prime numbers. For example the factors of 11 are 1 and 11 (only two factors)

We can see multiples in multiplication chart. Like the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32….. and it goes on n number of times


Important Fact about Factor and Multiple:

Suppose 5 × 4 = 20

So we can say that 5 and 4 are the factors of 20

Or, alternatively, 20 is a multiple of both 5 and 4

Hence, we can conclude that if a and b are two numbers then,

If a is divided by b then a is the factor of b

Again, if b is divisible by a, then b is the multiple of a


Difference between factors and multiples

1. Factors are finite in number that is a particular number has few number of factors

Multiples are infinite that is a particular number can have infinite number of multiples

2. The process to find factors is division and the process to find multiples is multiplication.

3. Factors are always less or equal to the given number whereas multiples are always greater than the given number.

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