How Can You Find All the Prime Factors of a Number Quickly?

The fastest way to find all the prime factors of a number is to start with the first prime number ($2$), and keep dividing by prime numbers until the entire number is broken down into its prime components.

For example, for the number $96$, the prime factors are:

$$ 2 \times 2 \times 2 \times 2 \times 2 \times 3 $$

Step-by-Step Prime Factorization of 96

Let’s find the prime factors of $96$ step by step:

  1. $96 \div 2 = 48$ → Add $2$
  2. $48 \div 2 = 24$ → Add $2$
  3. $24 \div 2 = 12$ → Add $2$
  4. $12 \div 2 = 6$ → Add $2$
  5. $6 \div 2 = 3$ → Add $2$
  6. $3$ is a prime number → Add $3$

You now have all the prime factors:

$$ \boxed{2 \times 2 \times 2 \times 2 \times 2 \times 3} $$

Final Check

Multiply the prime factors to confirm the result:

$$ 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 96 $$

✅ Correct!

Summary

To find the prime factorization of a number:

  • Start with the smallest prime ($2$)
  • Keep dividing while possible
  • Move to the next prime if needed
  • Stop when the remaining quotient is a prime

This method ensures a complete list of prime numbers that multiply to give your original number.

The prime factorization of 96 is:

$$ \boxed{2 \times 2 \times 2 \times 2 \times 2 \times 3} $$

Multiply to verify and confirm accuracy.