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". 

Apart from the stuff given above, if you want to know more about "Prime Factorization", please click here.

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

Related topics

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

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6