How Can You Find All the Prime Factors of a Number Quickly and Easily?

The fastest way to find all the prime factors of a number is to:

  1. Start with the first prime number, which is 2.
  2. Divide the number by that prime as many times as it divides evenly.
  3. Move to the next prime number when the previous one no longer divides.
  4. Repeat until the quotient becomes 1.

For example, the number 8 has prime factors: $$ 2, 2, 2 $$ because: $$ 2 \times 2 \times 2 = 8 $$

Find Prime Factors of 8

Let’s go through it step by step:

  • Start with the number 8.

  • First prime number is 2.

  • Is ( 8 \div 2 ) exact? Yes.

    Add 2 to the prime factor list.

    New quotient: $$ \frac{8}{2} = 4 $$

  • Is ( 4 \div 2 ) exact? Yes.

    Add another 2.

    New quotient: $$ \frac{4}{2} = 2 $$

  • Is ( 2 \div 2 ) exact? Yes.

    Add the final 2.

    New quotient: $$ \frac{2}{2} = 1 $$

Since we’ve reached 1, we stop.

Prime factors of 8: $$ 2, 2, 2 $$

Check:

$$ 2 \times 2 \times 2 = 8 $$

✔️ Correct!

Summary

To find the prime factorization of a number:

  1. Start with the smallest prime number: 2.
  2. Keep dividing by the same prime until it no longer divides evenly.
  3. Move to the next prime and repeat until the result is 1.

The prime factorization of 8 is: $$ 2 \times 2 \times 2 $$

Learning the first few prime numbers (up to 20) helps speed up the process: $$ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19 $$

Knowing these makes prime factorization quicker and easier.