Factors & Multiples 

Factors 

The numbers that we multiply to get a certain number are called its factors. 

For example, 2 × 5 = 10 

Here, both 2 and 5 are factors of 10. 

In the above example, we can see that 2 and 5 both can completely divide 10 without leaving any remainder. 

So, we can say that factors are “all of those numbers”that can divide “a given number” completely (meaning – the remainder should be 0 after division). 

Example - Write all the factors of 12. 

      Factors of 12 are 1, 2, 3, 4, 6 and 12 as each of these can completely divide 12. 

Multiples 

Are the numbers we get when we multiply any counting number by an integer, and are called its multiples. 

For example,6 × 5 = 30 

6 × 7 = 42 

Here, both 30 and 42 are multiples of 6. 

We can see in the above example, 30 is a multiple of 5 too and 42 is a multiple of 7 too. So, we can say 30 is a common multiple of 5 and 6, and 42 is a common multiple of 6 and 7. 

Example- Write 5 multiples of 12. 

Multiples of 12 are 12, 24, 36, 48, 60. 

Do Remember 

#Factors and multiples are inter-related with each other. Every number is a factor of its multiple. 

Example- If 18 is a multiple of 6, then 6 is a factor of 18. 

Prime Factorization 

When we express a composite number as a product of prime numbers, it is called prime factorization. The set of prime numbers are called the prime factors of the given number. 

Example-Let us take a number 24. 

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24. 

Out of these factors, the prime factors are 2 and 3. 

Now, let us express 24 as a product of its prime factors. 

So, 24 = 2 × 2 × 2 × 3 

Thus, prime factorization is expressing a number as a product of its prime factors.