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 smallest prime number (2), and keep dividing until all you’re left with are prime numbers. Multiply these together to reconstruct the original number.

For example, the prime factorization of 16 is:

$$ 2 \times 2 \times 2 \times 2 = 16 $$

Find Prime Factors of 16

Here is the step-by-step breakdown:

  1. Start with 16
    Divide by 2:
    $$ \frac{16}{2} = 8 $$
    ➡️ Add 2 to the list

  2. Divide 8 by 2:
    $$ \frac{8}{2} = 4 $$
    ➡️ Add 2 to the list

  3. Divide 4 by 2:
    $$ \frac{4}{2} = 2 $$
    ➡️ Add 2 to the list

  4. Divide 2 by 2:
    $$ \frac{2}{2} = 1 $$
    ➡️ Add 2 to the list

You’re done.

Prime Factor List

The prime factors of 16 are:

$$ 2, 2, 2, 2 $$

To verify:

$$ 2 \times 2 \times 2 \times 2 = 16 $$

✅ Confirmed!

Summary

To find the prime factors of any number:

  • Start with the smallest prime number (2)
  • Keep dividing until the quotient is 1
  • Every divisor used is a prime factor

So the prime factorization of 16 is:

$$ 2 \times 2 \times 2 \times 2 $$

Learn the first few prime numbers (up to 20) and this process becomes lightning-fast.