How can you quickly find the factors of a number?

Factors are numbers that divide into another number without leaving a remainder. They can never be greater than the number itself.

To find factors quickly:

  • Start with 1 and the number itself (since 1 always divides evenly).
  • Begin testing integers from 2 upwards.
  • If a number divides evenly, add both the divisor and its quotient to your list.
  • Stop once the checking number exceeds the square root of the original number.

If the number only has two factors (1 and itself), it’s a prime number.
If it has more than two, it’s a composite number.

To find the highest factor (other than the number itself), check the next biggest number in your factor list.

Find Factors of 30

Step-by-step method:

  1. Start your factor list: [1, 30]
  2. Check 2 → $30 \div 2 = 15$ → ✅ → add 2 and 15 → list: [1, 2, 15, 30]
  3. Check 3 → $30 \div 3 = 10$ → ✅ → add 3 and 10 → list: [1, 2, 3, 10, 15, 30]
  4. Check 4 → $30 \div 4$ leaves remainder → ❌
  5. Check 5 → $30 \div 5 = 6$ → ✅ → add 5 and 6 → list: [1, 2, 3, 5, 6, 10, 15, 30]
  6. Stop: You’ve passed √30 ≈ 5.47

All factors of 30:

$$ \boxed{1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30} $$

  • 30 has more than two factors → it is a composite number
  • The largest proper factor (not including 30) is 15

Summary

  • Factors of 30: $1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30$
  • Prime numbers have only 1 and itself as factors
  • Composite numbers have more than 2 factors
  • This factorization process is essential when simplifying fractions and solving number problems