PRIME FACTORIZATION

About "Prime Factorization"

Prime Factorization :

Prime factorization is the method of expressing a number as a product of prime numbers.

Usually we have two methods to find factors of a number.

(i) Prime factorization method

(ii) Factor tree method

Steps followed in the above method :

Step 1 : 

Put the given number inside the "L" shape 

Step 2 :

We have to split the given number by prime numbers only. That is,  always we have to put prime numbers out side the "L" shape.

Step 3 :

The tricks given below will be helpful to find the prime number which exactly divides the given number.

• A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.
• A number which ends with 0 or 5 is divisible by 5 
• If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

Step 4 :

Take the first digit of the given number and check how many times the prime number goes in to that. 

Further process is explained in the examples given below. 

Prime factorization - Example problems

Question 1 :

Find the prime factors of 324

Solution :

Step 1 :

Since the given number ends with 4, first we have to split the given number by the smallest even prime number 2.

Step 2 :

2 goes into 3 one time.We have 1 left. If we take this 1 along with the next digit 2, we get 12. If we divide this by 2, we get 6. 

We don’t have any number remaining in 12. So we can take the next digit 4. Again, if we divide 4 by 2, we get 2.

Step 2 :

If we repeat this process, we will get

So, the prime factors of 324 = 2 x 2 x 3 x 3 x 3 x 3 

Question 2 :

Find the prime factors of 625

Solution :

Step 1 :

Since the given number ends with 5, first we have to split it by the prime number 5.

Step 2 :

5 goes into 6 one time.We have 1 left. If we take this 1 along with the next digit 2, we get 12. Again we have to divide it by 5. If we divide this by 5, we get 2.

Now we have 2 left. Now we have to take this 2 along with the next digit 5, we get 25.  If we divide 25 by 5, we get 5.

Step 3 :

By repeating this process until we get prime factors. 

Hence, prime factors of 625 = 5 x 5 x 5 x 5

Question 3 :

Find the prime factors of 4096

Solution :

Prime factors of 4096

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 

Question 4 :

Find the prime factors of 400

Solution :

Prime factors of 400

= 2 x 2 x 2 x 2 x 5 x 5

Question 5 :

Find the prime factors of 144

Solution :

Prime factors of 144

= 2 x 2 x 2 x 2 x 3 x 3

Question 6 :

Find the prime factors of 1024

Solution :

Prime factors of 1024

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Question 7 :

Find the prime factors of 256

Solution :

Prime factors of 256

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Question 8 :

Find the prime factors of 2025

Solution :

Prime factors of 2025

= 5 x 5 x 3 x 3 x 3 x 3 

Question 9 :

Find the prime factors of 36

Solution :

Prime factors of 36

= 2 x 2 x 3 x 3

Question 10 :

Find the prime factors of 3136

Solution :

Prime factors of 3136

= 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7

After having gone through the stuff given above, we hope that the students would have understood "Prime Factorization". 

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• Finding square root by prime factorization methods
• Comparing surds
• Comparing fractions

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