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 continue dividing until the number is reduced entirely into prime numbers.

For example, for the number $90$, the prime factors are:

$$ 2 \times 3 \times 3 \times 5 $$

Step-by-Step Prime Factorization of 90

Let’s find the prime factors of $90$ step by step:

  1. $90 \div 2 = 45$ → Add $2$
  2. $45 \div 2$ → Not divisible
  3. Move to $3$
  4. $45 \div 3 = 15$ → Add $3$
  5. $15 \div 3 = 5$ → Add $3$
  6. $5 \div 3$ → Not divisible
  7. Test $4$ (not prime), skip
  8. $5$ is a prime and matches the remaining number → Add $5$

So the complete list of prime factors is:

$$ \boxed{2 \times 3 \times 3 \times 5} $$

Final Check

Multiply them together to verify:

$$ 2 \times 3 \times 3 \times 5 = 90 $$

✅ Correct!

Summary

To find the prime factors of a number:

  • Start at $2$
  • Keep dividing by each prime as long as it’s a factor
  • Once it no longer divides evenly, move to the next prime
  • Stop when the quotient is $1$

Knowing the first few prime numbers makes this process faster.

The prime factorization of 90 is:

$$ \boxed{2 \times 3 \times 3 \times 5} $$

Multiply all prime factors together to confirm the result.