# What is prime factorisation means? Explained with examples

Learn and know what is prime factorisation of a number in mathematics. In the lower classes especially for the classes 6, 7 and this is important concept. This concept will be helpful in solving many problems.

If you observe clearly, in the word factorisation there is word called “factor”. What is the meaning of a factor? Do you know it? If you know very good otherwise first meaning of a factor. After knowing what is a factor, then learn what is factorisation and after that learn what is prime factorisation. This is what you need to do before starting learning and knowing about what is prime factorisation?

## What is the meaning of factorisation? In math

Take any number and write it as the form of product of the factors then we say that we did factorisation.

For example, let us take one number 72. Now we need to write 72 as product of its factors. 72 is written as 9 × 8 i.e. 72 = 9 × 8. Now we say that we did factorisation of the number 72.

### What is meant by the Prime factorisation of the numbers?

We know that what is factorisation called? For any number while doing factorisation, if the factors are only the prime factors then we say it as a prime factorisation.

For example, the number 48 is written as product of the factors 2 and 3 i.e. 2 × 2 × 2 × 2 × 3 gives 48. In this factorisation, if we observe the factors then it is clear that all the factors are prime numbers. So we say that we did prime factorisation for the number 48.

Another example, the prime factorisation of the number 24 is? So 24 we need to write as product of only prime numbers. So 24 is written as 2 × 2 × 2 × 3.

#### How apply the prime factorisation method for the given number?

After learning what is prime factorisation, now we will learn how to do prime factorisation? Generally Prime factorisation can be done in the two ways. First one is if it is a small number we can write it very easily without doing anything. For this you should know the tables 1 to 20 at least.

The second method to do prime factorisation is by “L” division i.e. factorisation.

For example, how to do prime factorisation of 2744?

Observe the above image its showing step by step how to prime factorisation.

Write the number 2744 in the “L” shape and as 2744 is divisible exactly by the 2, so write 2 on left side of 2744.

In 2 table, 2744 goes 1372 times. So write 1372 below 2744.

Mark “L” shape again and left of 1372 write 2.

In table of 2, 1372 goes 686 times. So write 686 below 1372.

Mark “L” shape and to the left of 646, take 2.

In table of 2, 686 goes 343 times, so write 343 below 686.

Mark “L” and take 7 to the left of 343 because 7 divides 343 exactly.

In table of 7, 343 goes exactly 49 times. So write 49 below 343.

Now take 7 beside 49, as we know 49 goes 7 times exactly in the table of 7.

So write 7, below 49. Finally opposite to 7, to the left side take 7.

In table of 7, 7 goes 1 time so write 1 below 7, that’s it factorisation of 2744 is completed.

So finally we got the prime factorisation of  2744 i.e. ${ 2 }^{ 3 }$ × ${ 7 }^{ 3 }$ (we got 3 two’s and 3 sevens, so in exponential form we can write like this)

Hope now you have cleared all the doubts about what is prime factorisation and for what purpose the prime factorisation will be used.