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
= 2^{2}3^{4}
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
= 5^{4}
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
= 2^{12}
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
= 2^{4}5^{2}
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
= 2^{4}3^{2}
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
= 2^{10}
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
= 2^{8}
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
= 5^{2} 3^{4}
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
= 2^{2}3^{2}
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
= 2^{6}7^{2}
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