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:

  1. Start with 1 and your original number.
  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 the only factors are 1 and the number itself, the number is prime.
If there are more than two, the number is composite.

Let’s use this method to find the factors of 54.

Find Factors Of 54

Step-by-step:

  1. Start with: $[1, 54]$
  2. Try 2: $54 \div 2 = 27$ → ✅ → add 2 and 27 → $[1, 2, 27, 54]$
  3. Try 3: $54 \div 3 = 18$ → ✅ → add 3 and 18 → $[1, 2, 3, 18, 27, 54]$
  4. Try 4: $54 \div 4 = 13.5$ → ❌
  5. Try 5: $54 \div 5 = 10.8$ → ❌
  6. Try 6: $54 \div 6 = 9$ → ✅ → add 6 and 9 → $[1, 2, 3, 6, 9, 18, 27, 54]$
  7. Try 7: $54 \div 7 = 7.71\ldots$ → ❌
  8. You’ve reached $\sqrt{54} \approx 7.3$, so you can stop.

Final factor list:

$$ [1, 2, 3, 6, 9, 18, 27, 54] $$

  • 54 is a composite number because it has more than two factors.
  • The highest factor (excluding 54 itself) is 27.

Summary

The factors of 54 are: $[1, 2, 3, 6, 9, 18, 27, 54]$

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

Since 54 has many divisors, it is a composite number.