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 smallest prime number — 2.
  2. Try dividing the number.
  3. If it divides evenly, add it to your prime factor list and divide again.
  4. If not, move to the next prime.

For example, the number 15 has prime factors: $$ 3 \times 5 = 15 $$

Find Prime Factors of 15

Let’s break it down step-by-step:

  • Start with 15.

  • Try dividing by 2.

    $$ \frac{15}{2} = 7.5 \quad \text{(not a whole number)} $$

  • 2 is not a factor. Move to the next prime: 3.

    $$ \frac{15}{3} = 5 $$

✅ Add 3 to your prime factor list.

  • Try dividing 5 by 3:

    $$ \frac{5}{3} = 1.\overline{6} \quad \text{(not a whole number)} $$

  • Move to the next prime: 5.

    $$ \frac{5}{5} = 1 $$

✅ Add 5 to the list. You’re done.

Prime Factor List

The prime factors of 15 are:

$$ 3 \times 5 $$

To check your work:

$$ 3 \times 5 = 15 $$

✔️ Correct!

Summary

Prime factorization means finding all the prime numbers that multiply to give your original number.

For 15:

  • 2 didn’t work.
  • 3 did.
  • 5 did.

So:

$$ \text{Prime factors of } 15 = 3 \times 5 $$

Memorizing the first few prime numbers (up to 20) can make this process faster and easier:

$$ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19 $$