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

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 :

=  2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2

=  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 ⋅ 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 ⋅ 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 ⋅ 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 ⋅ 2 ⋅ 2 ⋅ 7 ⋅ 7

=  2⁶7²

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