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 your number.
  3. If it divides evenly, write it down and divide again.
  4. If it doesn’t, move to the next prime number.

For example, for the number 35, the prime factors are:

$$ 5 \times 7 = 35 $$

Find Prime Factors of 35

Here’s the step-by-step process:

  • Start with 35.

  • Can 2 divide 35?

    $$ \frac{35}{2} = 17.5 \quad \text{(not a whole number)} $$

  • Try 3:

    $$ \frac{35}{3} \approx 11.67 \quad \text{(no)} $$

  • Try 4:

    $$ \frac{35}{4} = 8.75 \quad \text{(no)} $$

  • Try 5:

    $$ \frac{35}{5} = 7 \quad \text{(yes)} $$

✅ Add 5 to your factor list.

Now check 7:

  • Is 7 prime? ✅ Yes.

  • Since:

    $$ \frac{7}{7} = 1 $$

✅ Add 7 to your factor list and you’re done.

Prime Factor List

So the prime factors of 35 are:

$$ 5 \times 7 $$

To check:

$$ 5 \times 7 = 35 $$

✔️ Confirmed.

Summary

To find the prime factorization of a number:

  • Divide by the smallest possible prime.
  • Keep going until you’re left with 1.
  • Record each prime used in the process.

The prime factors of 35 are:

$$ 5 \times 7 $$

Want to speed things up? Memorize the first few primes:

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

This makes checking factors much quicker!