Mastering Prime Factorization: Steps and Example of Prime Factorizing Numbers

Prime Factorization

Prime factorization is the process of expressing a composite number as a product of its prime factors

Prime factorization is the process of expressing a composite number as a product of its prime factors. The prime factors are the prime numbers that, when multiplied together, give the original number.

To find the prime factorization of a number, you need to follow these steps:

Step 1: Start with the smallest prime number, which is 2.

Step 2: Divide the given number by 2. If the number is divisible by 2, write down 2 as a factor and continue dividing the result by 2 until it’s no longer divisible by 2.

Step 3: Move to the next prime number, which is 3. Divide the current result by 3. If it is divisible by 3, write down 3 as a factor and continue dividing until it’s no longer divisible by 3.

Step 4: Repeat step 3 for the next prime numbers (5, 7, 11, 13, and so on) until you have completely factorized the number.

Step 5: Stop when the result becomes 1, as there are no more prime factors.

Let’s take an example to illustrate these steps.

Example: Find the prime factorization of 84.

Step 1: Starting with 2, we divide 84 by 2, which gives us 42. So, we have the factor 2.

Step 2: We continue dividing 42 by 2, giving us 21. Again, we have the factor 2.

Step 3: Dividing 21 by 2 is not possible, so we move on to the next prime number, which is 3. Dividing 21 by 3 gives us 7. We have the factor 3.

Step 4: As 7 is a prime number, we cannot divide it further.

Step 5: Since our result is 1, we stop.

Combining all the prime factors we found, we can express 84 as a product of its prime factors: 2 x 2 x 3 x 7.

So, the prime factorization of 84 is 2^2 x 3 x 7.

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