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. Continue dividing the original number by prime numbers in ascending order.
  3. Stop once the quotient becomes 1.

For example, the number 10 has prime factors: $$ 2 \times 5 = 10 $$

Find Prime Factors of 10

Let’s find the prime factorization of 10 step by step:

  • Start with 10.

  • First prime number is 2.

  • Can 2 divide 10 evenly?

    Yes. Add 2 to the prime factor list.

    Now divide: $$ \frac{10}{2} = 5 $$

  • Can 2 divide 5?

    No — remainder ≠ 0.

  • Try the next prime number: 3.

    Is 3 prime? Yes.

    Can 3 divide 5?

    No — remainder ≠ 0.

  • Try next prime: 4.

    Is 4 prime? No. Skip.

  • Next prime: 5.

    Is 5 prime? Yes.

    Does 5 divide 5?

    Yes. Add 5 to the list.

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

You’ve reached 1 — so you’re done.

✅ Prime factors of 10 are: $$ 2 \times 5 $$

Check:

$$ 2 \times 5 = 10 $$

✔️ Confirmed!

Summary

To perform prime factorization:

  1. Start dividing by the smallest prime (2).
  2. Continue dividing until the result is 1.
  3. If a prime number doesn’t divide evenly, move to the next one.

Memorizing the first few primes can make the process faster: $$ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19 $$

For 10, the prime factorization is: $$ 2 \times 5 $$

Multiply your results to verify the original number.