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
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