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

The fastest way is to start with the smallest prime number (2) and keep dividing until all that’s left are prime numbers. Multiply these together to reconstruct the original number.

For example, the prime factorization of 20 is:

$$ 2 \times 2 \times 5 = 20 $$

Step-by-step: Prime Factors of 20

  1. Start with 20
    $$ \frac{20}{2} = 10 $$
    ➡️ Add 2 to the list.

  2. Divide 10 by 2:
    $$ \frac{10}{2} = 5 $$
    ➡️ Add another 2 to the list.

  3. 5 is not divisible by 2, so try the next primes.

    • 3? No.
    • 5? Yes.
      $$ \frac{5}{5} = 1 $$
      ➡️ Add 5 to the list.

You’re done when the quotient is 1.

Prime Factor List

The prime factors of 20 are:

$$ 2, 2, 5 $$

To check:

$$ 2 \times 2 \times 5 = 20 $$

✅ Correct!

Summary

To find the prime factors of a number:

  • Begin with the smallest prime (2)
  • Keep dividing and replacing the number with the quotient
  • Add each divisor to your list
  • Stop when you’re left with 1

Memorize the first few primes (e.g., 2, 3, 5, 7, 11…) to make the process quicker.

The prime factorization of 20 is:

$$ 2 \times 2 \times 5 $$