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 begin with the smallest prime number ($2$) and divide repeatedly. Continue moving through the sequence of prime numbers until the quotient becomes $1$.
For example, the prime factors of $120$ are:
$$ 2 \times 2 \times 2 \times 3 \times 5 $$
Step-by-Step Prime Factorization of 120
Let’s find the prime factors of 120 step by step:
Start with the first prime: $2$
$120 \div 2 = 60$ → divisible
Add $2$ to the list.$60 \div 2 = 30$
Add $2$ to the list again.$30 \div 2 = 15$
Add another $2$ to the list.$15 \div 2$ → not divisible (remainder 1)
Move to the next prime number: $3$$15 \div 3 = 5$
Add $3$ to the list.$5 \div 3$ → not divisible
Next prime is $5$$5 \div 5 = 1$
Add $5$ to the list.
You now have the complete list of prime factors of 120:
$$ \boxed{2 \times 2 \times 2 \times 3 \times 5} $$
Final Check
Multiply the prime factors:
$$ 2 \times 2 \times 2 \times 3 \times 5 = 120 $$
✅ The product matches the original number.
Summary
To find the prime factors of a number:
- Start with $2$ and divide as many times as possible.
- Move to the next prime when you can’t divide cleanly anymore.
- Repeat until you reach $1$.
Tip:
Memorizing the first few prime numbers (up to $20$) makes this process much faster.
The prime factorization of $120$ is:
$$ \boxed{2 \times 2 \times 2 \times 3 \times 5} $$
You can always check by multiplying all prime factors to get back the original number.