How can you quickly find the factors of a number?

Factors are numbers that divide evenly into another number — that is, without leaving a remainder — and they can never be larger than the number itself.

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

Since 1 divides into every number, we can include it by default, along with the number itself.

From there:

  • Start checking from 2 onward.
  • If a number divides evenly into the original, add both the divisor and its quotient.
  • Stop once your check number exceeds the square root of the original.

If only 1 and the number itself are factors, the number is prime.
If more are found, the number is composite.

The largest factor other than the number itself is easily spotted by reviewing the factor list.

Find Factors of 24

Step-by-step process:

  1. Start with [1, 24] in your list.
  2. Check 2 → $24 \div 2 = 12$ → ✅ → add 2 and 12 → list: [1, 2, 12, 24]
  3. Check 3 → $24 \div 3 = 8$ → ✅ → add 3 and 8 → list: [1, 2, 3, 8, 12, 24]
  4. Check 4 → $24 \div 4 = 6$ → ✅ → add 4 and 6 → list: [1, 2, 3, 4, 6, 8, 12, 24]
  5. Stop: You’ve passed the square root of 24 (~4.9)

So the factors of 24 are:

$$ \boxed{1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24} $$

  • 24 has more than 2 factors → it is a composite number
  • The largest factor (excluding 24) is 12

Summary

  • Factors of 24: $1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24$
  • Prime numbers have only two factors: 1 and itself
  • Composite numbers have more than two factors
  • Finding factors quickly is useful for simplifying fractions and solving divisibility problems