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 until you’re left with only prime numbers. These prime numbers, when multiplied together, give you the original number.

For example, for the number $80$, the prime factors are:

$$ 2 \times 2 \times 2 \times 2 \times 5 $$

Step-by-Step Prime Factorization of 80

Let’s find the prime factors of $80$ step by step:

  1. $80 \div 2 = 40$ → Add $2$
  2. $40 \div 2 = 20$ → Add another $2$
  3. $20 \div 2 = 10$ → Add another $2$
  4. $10 \div 2 = 5$ → Add another $2$
  5. $5 \div 2$ → Not divisible
  6. Try the next prime: $3$ → $5 \div 3$ → Not divisible
  7. $4$ is not prime
  8. $5$ is prime and $5 \div 5 = 1$ → Add $5$

So the complete list of prime factors of $80$ is:

$$ \boxed{2 \times 2 \times 2 \times 2 \times 5} $$

Final Check

Multiply them together:

$$ 2 \times 2 \times 2 \times 2 \times 5 = 80 $$

✅ Correct!

Summary

To find the prime factors of a number:

  • Start with $2$, the smallest prime
  • Divide repeatedly until you can’t anymore
  • Move to the next prime
  • Continue until the quotient is $1$

Knowing the first few prime numbers (up to $20$) makes the process much faster.

The prime factorization of $80$ is:

$$ \boxed{2 \times 2 \times 2 \times 2 \times 5} $$

Multiply them together to verify your result.