Prime Factorization

PRIME FACTORIZATION:

Writing a number as a product of its factors is called Factorization.

If we write a number as a product of its Prime factors, it is called Prime Factorization.

There are two methods to find the Prime factors of a number. They are:

(i) Factor tree method

(ii) Short division method.

(i) FACTOR TREE METHOD:

A factor tree shows the prime factors of a composite number in a “tree-like” form.

·        In this method, we factorize the numbers in such a way that at least one of the factors is prime factor.

·        We then factorize the composite factor further to get at least one prime factor.

·        We continue this way until all the factors we get are prime factors.

·        We can make different factor trees to find the same prime factorization.

1) 100.

Answer:

The two different factor trees for number 100:

 

Here, the factors trees gives same Prime Factorization.

Prime factors of number 100 : 2 * 2 * 5 * 5.

 

2)  72.

Answer:

The different factor trees are:

 

The different factor trees gives same Prime Factorization.

The prime factors of number 72  are : 2* 2* 2 * 3* 3.

3) 60

Answer:

The different factor trees are:

The different factor trees gives same Prime Factorization.

The Prime factors of number 60  are :  2* 2 * 3 * 5.

(ii) SHORT DIVISION METHOD:

We follow the below steps to find factors in this method. We have to use only Prime numbers to divide the number.

Step-1: First we divide the number by the smallest prime number which divides the number exactly.

Step-2: We divide the obtained quotient in step-1 again by the smallest or the next smallest prime number if it is not exactly divisible by the smallest prime number.

We repeat the process again and again till the quotient becomes 1.

Step-3: We multiply all the prime factors obtained, which gives the Number itself.

 

1) 32

Answer:

Step-1 : The number 32 is dividend. Dividing 32 with the smallest Prime number : 2, which divides exactly and leaves quotient as 16.

Step-2 : Now the new dividend is 16, which is divided exactly by the smallest prime number 2  again. This division process is continued till we get the quotient as 1.

Step-3: We multiply all the prime factors obtained, which gives the Number itself.

The factors of  32 are: 2 * 2 * 2* 2* 2.

 

2) 45.

Answer:

Step-1: The smallest prime number is 2. But it cannot divide 45 exactly. So, we go for the next smallest prime number, 3 which divides 45 exactly.

Step-2: The new dividend is 15, which again divided by the smallest prime number. This process is to be continued till quotient 1.

Step-3 : We multiply all the prime factors obtained, which gives the Number itself.

 

The factors of  45  are:  3 * 3 * 5.