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 start with the first prime number (2), and divide repeatedly until the remaining number is 1.

For example, the prime factorization of 300 is:

$$ 2 \times 2 \times 3 \times 5 \times 5 = 300 $$

Find Prime Factors of 300

Step-by-step breakdown:

  1. Start with 300
    Divide by 2:
    $$ \frac{300}{2} = 150 $$
    ➡️ Add 2 to the list

  2. Divide 150 by 2:
    $$ \frac{150}{2} = 75 $$
    ➡️ Add 2 to the list

  3. 75 is not divisible by 2. Try next prime, 3:
    $$ \frac{75}{3} = 25 $$
    ➡️ Add 3 to the list

  4. 25 is not divisible by 3 or 4. Try 5:
    $$ \frac{25}{5} = 5 $$
    ➡️ Add 5 to the list

  5. Divide 5 by 5:
    $$ \frac{5}{5} = 1 $$
    ➡️ Add 5 to the list

You’re done!

Prime Factor List

The prime factors of 300 are:

$$ 2, 2, 3, 5, 5 $$

To check:

$$ 2 \times 2 \times 3 \times 5 \times 5 = 300 $$

✅ Verified.

Summary

To find the prime factors of a number:

  • Start dividing by 2 and move up through the prime numbers
  • Record each divisor when division leaves no remainder
  • Stop once the quotient is 1

So the prime factorization of 300 is:

$$ 2 \times 2 \times 3 \times 5 \times 5 $$

Memorizing prime numbers up to 20 can help speed up this process.