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

The fastest way is to start dividing the number by the smallest prime, which is 2, and continue dividing by primes until the result is 1.

For example, the prime factorization of 32 is:

$$ 2 \times 2 \times 2 \times 2 \times 2 = 32 $$

Step-by-step: Prime Factors of 32

  1. Start with 32

  2. Divide by 2: $$ \frac{32}{2} = 16 $$ Add 2 to the factor list.

  3. Divide 16 by 2: $$ \frac{16}{2} = 8 $$ Add another 2.

  4. Divide 8 by 2: $$ \frac{8}{2} = 4 $$ Add another 2.

  5. Divide 4 by 2: $$ \frac{4}{2} = 2 $$ Add another 2.

  6. Divide 2 by 2: $$ \frac{2}{2} = 1 $$ Add the final 2.

✅ You have now reached 1, so you’re done.

Prime Factor List

The prime factors of 32 are:

$$ 2, 2, 2, 2, 2 $$

Or written with exponents:

$$ 2^5 = 32 $$

Summary

To find the prime factorization of a number:

  • Begin dividing by the smallest prime: 2
  • Keep dividing and adding to the list
  • Stop when the quotient becomes 1
  • Use exponent notation to simplify repeated factors

So, the prime factorization of 32 is:

$$ 2^5 $$

To verify:

$$ 2 \times 2 \times 2 \times 2 \times 2 = 32 $$

✔️ Correct!