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How to do Prime Factorization?

Published in Math 2 mins read

Prime factorization is breaking down a composite number into a product of its prime factors. Here's how to do it:

1. Understand Prime Numbers:

  • A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, etc.

2. Choose a Method:

There are two common methods:

  • Factor Tree Method
  • Division Method

3. Factor Tree Method:

This method visually represents the factorization process.

  • Start with the number you want to factor. Write it at the top.
  • Find any two factors of the number. Draw two branches downward, and write the factors at the end of each branch.
  • Check if the factors are prime. If a factor is prime, circle it.
  • If a factor is not prime, repeat the process – find two factors of that number and draw branches.
  • Continue until all factors at the ends of the branches are prime numbers.
  • Write out the prime factors. The prime factorization is the product of all the circled prime numbers.

Example: Prime factorization of 36

        36
       /  \
      4    9
     / \  / \
    2  2 3  3

Therefore, the prime factorization of 36 is 2 x 2 x 3 x 3, or 22 x 32.

4. Division Method:

This method involves repeatedly dividing the number by prime numbers.

  • Start with the number you want to factor.
  • Divide the number by the smallest prime number that divides it evenly. (Usually, start with 2, then 3, 5, 7, and so on).
  • Write down the prime number you divided by.
  • Divide the quotient (the result of the division) by the smallest prime number that divides it evenly.
  • Repeat this process until the quotient is 1.
  • Write out the prime factors. The prime factorization is the product of all the prime numbers you divided by.

Example: Prime factorization of 36

  • 36 ÷ 2 = 18
  • 18 ÷ 2 = 9
  • 9 ÷ 3 = 3
  • 3 ÷ 3 = 1

Therefore, the prime factorization of 36 is 2 x 2 x 3 x 3, or 22 x 32.

5. Verify Your Answer:

  • Multiply all the prime factors together. The result should be the original number.

In summary, prime factorization involves finding the prime numbers that multiply together to give you the original number. Both the factor tree and division methods are effective ways to achieve this.

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