How can you quickly find the factors of a number?

Factors are numbers that divide into another number without leaving a remainder. A factor is always less than or equal to the original number.

To find factors quickly, follow this process:

  1. Start with 1 and your original number — these are always factors.
  2. Begin testing numbers from 2 upwards:
    • Ask: Does this number divide into the original number with no remainder?
    • If yes, add both the divisor and its quotient to your list.
  3. Stop once your test number exceeds the square root of the original number.

If your final list contains only 1 and the original number, then the number is prime.

If your list contains more than two factors, the number is a composite number.

To find the highest factor other than the number itself, simply pick the largest value in the list that is not the original number.

Let’s see this in action.

Find Factors Of 8

Step-by-step:

  1. Start your list: $[1, 8]$
  2. Try 2: $8 \div 2 = 4$ → no remainder → ✅
  3. Add both 2 and 4: $[1, 2, 4, 8]$
  4. Stop here — you’ve passed the square root of 8.
  5. Final factor list: $[1, 2, 4, 8]$
  6. Since there are more than 2 factors, 8 is a composite number.
  7. The highest factor (excluding 8 itself) is 4.

Summary

The factors of a number are all the values that divide evenly into it, from 1 up to the number itself.

  • Factors of 8: $[1, 2, 4, 8]$
  • 8 is a composite number, because it has more than 2 factors.
  • A number with exactly two factors — 1 and itself — is a prime number.