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

The following steps would be useful to write a number as a product of its prime factors

Step 1 : 

Decompose the given number into prime factors using synthetic division.

Step 2 :

Write all the prime factors as a product. If the same prime factor is repeated, write it as a power of that factor.

Example 1 :

Express 324 as the product of its prime factors.

Solution :

Decompose 324 as into prime factors as shown below. 

Product of the prime factors of 324 :

= 2  2  3  3  3  3 

  =  2234

Example 2 :

Express 625 as the product of its prime factors

Solution :

Decompose 625 as into prime factors as shown below. 

Product of the prime factors of 625 :

  =  5 ⋅ 5 ⋅ 5  5

=  54

Example 3 :

Express 4096 as the product of prime its factors.

Solution :

Decompose 4096 as into prime factors as shown below. 

Product of the prime factors of 4096 :

=  222222222222

=  212

Example 4 :

Express 400 as the product of its prime factors.

Solution :

Decompose 400 as into prime factors as shown below. 

Product of the prime factors of 400 :

=  2 ⋅  2  2  5 ⋅ 5

=  2452

Example 5 :

Express 144 as the product of its prime factors

Solution :

Decompose 144 as into prime factors as shown below. 

Product of the prime factors of 144 :

=  2 ⋅  2  2  3 ⋅ 3

=  2432

Example 6 :

Express 1024 as the product of its prime factors.

Solution :

Decompose 1024 as into prime factors as shown below. 

Product of the prime factors of 1024 :

=  2  2  2 ⋅  2  2  2  2  2  2

=  210

Example 7 :

Express 256 as the product of its prime factors.

Solution :

Decompose 256 as into prime factors as shown below. 

Product of the prime factors of 256 :

=  2  2  2  2  2 ⋅ 2 ⋅ 2  2

=  28

Example 8 :

Express 2025 as the product of its prime factors.

Solution :

Decompose 2025 as into prime factors as shown below. 

Product the prime factors of 2025 :

=  5  5  3  3  3 ⋅ 3

=  52 34

Example 9 :

Express 36 as the product of its prime factors

Solution :

Decompose 36 as into prime factors as shown below. 

Product of the prime factors of 36 :

=  2 ⋅ 2 ⋅ 3  3

=  2232

Example 10 :

Express 3136 as the product of its prime factors.

Solution :

Decompose 3136 as into prime factors as shown below. 

Product of the prime factors of 3136 :

=  2  2  2    2   7

=  2672

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