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), and divide repeatedly until the remaining number is 1.

For example, the prime factorization of 70 is:

$$ 2 \times 5 \times 7 = 70 $$

Find Prime Factors of 70

Step-by-step breakdown:

  1. Start with 70
    Divide by 2:
    $$ \frac{70}{2} = 35 $$
    ➡️ Add 2 to the list.

  2. Try 2 again:
    $$ \frac{35}{2} = 17.5 $$
    ➡️ Not divisible. Try the next prime: 3

  3. Try 3:
    $$ \frac{35}{3} \approx 11.67 $$
    ➡️ Not divisible. Try the next prime: 5

  4. Divide by 5:
    $$ \frac{35}{5} = 7 $$
    ➡️ Add 5 to the list.

  5. Try 5 again:
    $$ \frac{7}{5} = 1.4 $$
    ➡️ Not divisible. Try the next prime: 7

  6. Divide by 7:
    $$ \frac{7}{7} = 1 $$
    ➡️ Add 7 to the list. You’re done!

Prime Factor List

The prime factors of 70 are:

$$ 2, 5, 7 $$

To check:

$$ 2 \times 5 \times 7 = 70 $$

✅ Verified.

Summary

To find the prime factors of a number:

  • Start dividing by 2 and move up through the prime numbers
  • Record each divisor when division leaves no remainder
  • Stop once the quotient is 1

So the prime factorization of 70 is:

$$ 2 \times 5 \times 7 $$

Memorizing prime numbers up to 20 can help speed up this process.