HOW TO EXPRESS A NUMBER AS THE PRODUCT OF ITS PRIME FACTORS

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

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.

Example 1 :

Express 324 as the product of prime factors

Solution :

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

If we repeat this process, we get

So, the prime factors of 324

= 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 

  =  2²3⁴

Example 2 :

Express 625 as the product of prime factors

Solution :

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

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.

By repeating this process until we get prime factors. 

Prime factors of 625 :

  =  5 ⋅ 5 ⋅ 5 ⋅ 5

=  5⁴

Example 3 :

Express 4096 as the product of prime factors.

Solution :

Prime factors of 4096 :

=  2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2

=  2¹²

Example 4 :

Express 400 as the product of prime factors.

Solution :

Prime factors of 400 :

=  2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5

=  2³5²

Example 5 :

Express 144 as the product of prime factors

Solution :

Prime factors of 144 :

=  2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3

=  2³3²

Example 6 :

Express 1024 as the product of prime factors.

Solution :

Prime factors of 1024 :

=  2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

=  2¹⁰

Example 7 :

Express 256 as the product of prime factors.

Solution :

Prime factors of 256 :

=  2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

=  2⁸

Example 8 :

Express 2025 as the product of prime factors.

Solution :

Prime factors of 2025 :

=  5 ⋅ 5 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3

=  5² 3⁴

Example 9 :

Express 36 as the product of prime factors

Solution :

Prime factors of 36 :

=  2 ⋅ 2 ⋅ 3 ⋅ 3

=  2²3²

Example 10 :

Express 3136 as the product of prime factors.

Solution :

Prime factors of 3136 :

=  2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7 ⋅ 7

=  2⁶7²

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