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 $81$, the prime factors are:

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

Step-by-Step Prime Factorization of 81

Let’s find the prime factors of $81$ step by step:

  1. $81 \div 2$ → Not divisible (remainder $1$)
  2. Try the next prime: $3$
  3. $81 \div 3 = 27$ → Add $3$
  4. $27 \div 3 = 9$ → Add $3$
  5. $9 \div 3 = 3$ → Add $3$
  6. $3 \div 3 = 1$ → Add $3$ and stop

So the complete list of prime factors is:

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

Final Check

Multiply them together to verify:

$$ 3 \times 3 \times 3 \times 3 = 81 $$

✅ 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 81 is:

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

Multiply all prime factors together to confirm the result.