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Prime Factorization Examples

Prime numbers, as we know, are the positive numbers bigger than 1, which are not divisible by any number except itself and 1. Every number can be represented as the product of prime numbers. These prime numbers are known as prime factors for that particular number. Prime factorization is the method of finding prime factors for a number. The set of prime factors for a particular number is always unique.

Few examples of prime factorization technique are illustrated below:

Example 1: Determine prime factors of 45.
Solution: Prime factorization process for 45 is illustrated below:
Prime Factorization
Hence, prime factors of 45 are 3 $\times$ 3 $\times$ 5.

Example 2: Calculate prime factors of 126.
Solution: Prime factorization process for 126 is shown below:
Prime Factor Example
Hence, prime factors of 126 are 2 $\times$ 3 $\times$ 3 $\times$ 7.

Example 3: Determine prime factors of 84.
Solution: Prime factorization of 84 is demonstrated down:
Prime Factorization Example
Hence, prime factors of 84 are 2 $\times$ 2 $\times$ 3 $\times$ 7.

Example 4: Find prime factors of 3250.
Solution: Prime factorization of 3250 is illustrated below:
Prime Factor
Hence, prime factors of 3250 are 2 $\times$ 5 $\times$ 5 $\times$ 5 $\times$ 13.

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