How can you quickly find the factors of a number?

Factors are the numbers that divide into another number without leaving a remainder and can never be bigger than the original number.

To find factors quickly, start with the number 1 and ask yourself:
Can this number divide into the original number without leaving a remainder?

Since 1 divides into every number, you can begin checking from 2 — knowing your factor list already includes 1 and the original number.

Increment your number by 1 each time, and ask the same question.
If the division works, add both the divisor and the quotient to your factor list.

You can stop once your test number exceeds the square root of the original number.

If the only factors you find are 1 and the number itself, then your number is a prime number.
If you find more, it’s a composite number.

To find the highest factor other than the number itself, simply look at the second-largest value in your list.

Find Factors of 12

Step-by-step:

  1. Begin with 1 and 12 → factor list: [1, 12]
  2. Try 2 → $12 \div 2 = 6$ → ✅ → add 2 and 6 → factor list: [1, 2, 6, 12]
  3. Try 3 → $12 \div 3 = 4$ → ✅ → add 3 and 4 → factor list: [1, 2, 3, 4, 6, 12]
  4. Stop here — you’ve passed the square root of 12 (~3.46)

So the factors of 12 are:

$$ \boxed{1,\ 2,\ 3,\ 4,\ 6,\ 12} $$

  • Since there are more than 2 factors, 12 is a composite number
  • The highest factor other than 12 is 6

Summary

  • Factors of 12: $1,\ 2,\ 3,\ 4,\ 6,\ 12$
  • A number is prime if it has only 2 factors (1 and itself)
  • A number is composite if it has more than 2 factors
  • This method is fast, logical, and works for any positive integer