How can you find all the prime factors of a number quickly and easily?

The fastest method is to start with the smallest prime number (2), and keep testing prime numbers until the number is completely broken down into prime components.

For example, the prime factorization of 30 is:

$$ 2 \times 3 \times 5 = 30 $$

Step-by-step: Prime Factors of 30

  1. Start with 30

  2. Check divisibility by 2:
    $$ \frac{30}{2} = 15 $$
    ➡️ Add 2 to the list.

  3. Try 2 again:
    $$ \frac{15}{2} $$ leaves a remainder → not divisible.

  4. Try next prime: 3
    $$ \frac{15}{3} = 5 $$
    ➡️ Add 3 to the list.

  5. Try 3 again:
    $$ \frac{5}{3} $$ leaves a remainder → not divisible.

  6. Next prime: 5
    $$ \frac{5}{5} = 1 $$
    ➡️ Add 5 to the list. Done!

Prime Factor List

The prime factors of 30 are:

$$ 2, 3, 5 $$

Check:

$$ 2 \times 3 \times 5 = 30 $$

✅ Correct!

Summary

To find the prime factors of a number:

  • Start with the smallest prime (2)
  • Keep dividing by primes and collecting them in a list
  • When you’re left with 1, you’re finished

Knowing the first 10–20 prime numbers helps make this process much faster.

The prime factorization of 30 is:

$$ 2 \times 3 \times 5 $$