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 method:

  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 factor list contains only 1 and the number itself, then it’s a prime number.

If it contains more than two numbers, it’s a composite number.

Let’s try this method for the number 32.

Find Factors Of 32

Step-by-step:

  1. Start with: $[1, 32]$
  2. Try 2: $32 \div 2 = 16$ → ✅ → add 2 and 16 → $[1, 2, 16, 32]$
  3. Try 3: $32 \div 3 = 10.66\ldots$ → ❌
  4. Try 4: $32 \div 4 = 8$ → ✅ → add 4 and 8 → $[1, 2, 4, 8, 16, 32]$
  5. Try 5: $32 \div 5 = 6.4$ → ❌
  6. You’ve now passed $\sqrt{32} \approx 5.6$, so you can stop.

The final list of factors is:

$$ [1, 2, 4, 8, 16, 32] $$

  • Since there are more than two factors, 32 is a composite number.
  • The highest factor (excluding 32 itself) is 16.

Summary

The factors of 32 are: $[1, 2, 4, 8, 16, 32]$

  • A prime number has exactly two factors: 1 and itself.
  • A composite number has more than two factors.

Since 32 has multiple divisors beyond 1 and itself, it is a composite number.