Prime factorization (Prime Decomposition)

Prime numbers are those numbers which can be divided only by 1 or itself. Prime numbers are basic building blocks of all numbers.

For example: 2, 3, 5, 7, 9 etc…

These numbers can’t be divided by any other number.

Prime factorization means factorized the number till we are not getting the prime numbers. We can say it is set of prime numbers which multiply together to give original number.

Lets us take example of 76:

Another method is tree method

**Common factorization**

**Introduction :**

The Factors are the numbers which we multiply together to get another number.

When we find the factors of two or more numbers, and then find some factors are the same (“common”), then they are the “common factors”.

**Rules to solve Common Factorization:**

**.** Firstly we have to check the whole equation. Check that all the numbers are “Even” . If yes then we can take 2 as common. Because all even number are divisible by “2”.

. If there is any odd number also then we can’t take 2 as a common.

. After this check Is there any same variable is there? If yes then we take that as common.

. Then in the last step we just take the common number and variable as outside.

**Example **: 15 and 35

2m+2n In this question what is common its 2. So that means

We can take 2 as outside so it become like:

2m+2n = 2(m+n)

And if we have a question like:

6x^{2 }+ 36x + 12xy

In this Question see we you can take 6 as common because we know that 36 and 12 both can be divided by 6. So take 6 as common:

6(x^{2} +6x +2xy)

Now inside the bracket as you can see there is one more thing that is common its “x”. So we can also take “x” as common

6x(x +6 +2y)

So 6x is common here so this known as “COMMON FACTORISATION”.

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