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 entire number has been reduced to a list of prime numbers.

For example, for the number $100$, the prime factors are:

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

Step-by-Step Prime Factorization of 100

Let’s find the prime factors of $100$ step by step:

  1. $100 \div 2 = 50$ → Add $2$
  2. $50 \div 2 = 25$ → Add another $2$
  3. $25 \div 2$ → Not divisible
  4. Try the next prime: $3$ → $25 \div 3$ → Not divisible
  5. $4$ is not prime
  6. $5 \div 25 = 5$ → Add $5$
  7. $5 \div 5 = 1$ → Add another $5$

So the complete list of prime factors of $100$ is:

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

Final Check

Multiply them together to verify:

$$ 2 \times 2 \times 5 \times 5 = 100 $$

✅ Correct!

Summary

To find the prime factors of a number:

  • Start with $2$
  • Keep dividing until no longer divisible
  • Move to the next prime
  • Repeat until the quotient becomes $1$

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

The prime factorization of 100 is:

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

Multiply all prime factors together to confirm the result.