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 you’re left with only primes. Multiply all the primes you found together and you’ll recover your original number.

For example, the prime factorization of 27 is:

$$ 3 \times 3 \times 3 = 27 $$

Step-by-step: Prime Factors of 27

  1. Start with 27

  2. Check divisibility by 2:
    Not divisible.

  3. Try the next prime: 3
    $$ \frac{27}{3} = 9 $$
    ➡️ Add 3 to the list.

  4. Divide 9 by 3:
    $$ \frac{9}{3} = 3 $$
    ➡️ Add another 3 to the list.

  5. Divide 3 by 3:
    $$ \frac{3}{3} = 1 $$
    ➡️ Add one final 3.

Now that you’re left with 1, you’re done.

Prime Factor List

The prime factors of 27 are:

$$ 3, 3, 3 $$

To check:

$$ 3 \times 3 \times 3 = 27 $$

✅ Correct!

Summary

To find the prime factors of any number:

  • Start with the smallest prime: 2
  • Divide the number by the prime if it goes evenly
  • Add the prime to your list
  • Replace the number with the quotient and repeat
  • Stop once the quotient becomes 1

Memorizing prime numbers up to 20 (like 2, 3, 5, 7, 11, 13, 17, 19) will help you go faster.

The final result:

$$ \text{Prime factorization of 27} = 3 \times 3 \times 3 $$