How can you find all the prime factors of a number quickly and easily?
The fastest way to find all the prime factors of a number is to start with the first prime number (2), then keep dividing until you’re left with only prime numbers.
For example, for the number 64 the prime factorization is:
$$ 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64 $$
Find Prime Factors of 64
Let’s go step-by-step:
Start with 64
Divide by 2:
$$ \frac{64}{2} = 32 $$
➡️ Add 2 to the list.
Divide again:
$$ \frac{32}{2} = 16 $$
➡️ Add 2.
Again:
$$ \frac{16}{2} = 8 $$
➡️ Add 2.
Continue:
$$ \frac{8}{2} = 4 $$
➡️ Add 2.
Then:
$$ \frac{4}{2} = 2 $$
➡️ Add 2.
Finally:
$$ \frac{2}{2} = 1 $$
➡️ Add 2 and stop.
Prime Factor List
The prime factors of 64 are:
$$ 2 \times 2 \times 2 \times 2 \times 2 \times 2 $$
✔️ To verify:
$$ 2^6 = 64 $$
Summary
To perform a prime factorization:
- Start at 2 and divide repeatedly
- Add each divisor to your factor list
- Stop when the quotient is 1
So for 64, we get:
$$ 2^6 = 64 $$
The prime factor list is: 2, 2, 2, 2, 2, 2
Memorizing prime numbers up to 20 can speed up this process.