Learn How to Find the Prime Factorization of a Number with Easy Steps.

Prime Factorization

To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime

Prime factorization is the process of breaking down a composite number into its prime factors. A prime factor is a prime number that can divide the composite number without leaving a remainder.

To find the prime factorization of a composite number, you can follow these steps:

Step 1: Find a factor of the composite number that is prime. If the number itself is prime, then it is its own prime factorization.

Step 2: Divide the composite number by the prime factor you found in Step 1.

Step 3: Repeat Steps 1 and 2 with the quotient obtained from Step 2 until you get a quotient that is a prime number.

Step 4: Write down the prime factors obtained in Steps 1 to 3 and multiply them together to get the prime factorization of the original composite number.

For example, let’s find the prime factorization of 120:

Step 1: The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The prime factors are 2, 3, 5, and 1.

Step 2: 120 ÷ 2 = 60.

Step 3: 60 ÷ 2 = 30. 30 ÷ 2 = 15. 15 is a prime number.

Step 4: The prime factors are 2, 2, 2, 3, and 5. Multiplying them together we get: 2 x 2 x 2 x 3 x 5 = 120.

Therefore, the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.

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