How can you quickly find the factors of a number?

Factors are the numbers that divide evenly into another number — that is, with no remainder.

Factors are never greater than the number itself. To find all the factors of a number:

  1. Start at 1 — since 1 is a factor of every number.
  2. Then try 2, 3, 4, and so on.
  3. Stop once you reach or pass the square root of the number.

Let’s go through this process step-by-step for the number 29.

Finding Factors of 29

  1. Begin with the factor list: $[1, 29]$
  2. Try 2: $29 \div 2 = 14.5$ → remainder → ❌
  3. Try 3: $29 \div 3 = 9.66\ldots$ → remainder → ❌
  4. Try 4: $29 \div 4 = 7.25$ → remainder → ❌
  5. Try 5: $29 \div 5 = 5.8$ → remainder → ❌
  6. You’ve now passed $\sqrt{29} \approx 5.38$, so you can stop.

Since no other numbers divide evenly into 29, the only factors are:

$$ [1, 29] $$

This means 29 is a prime number — it has exactly two factors: 1 and itself.

Summary

The factors of 29 are: $[1, 29]$

Because 29 has no divisors other than 1 and itself, it is classified as a prime number.

The more often you practise this factor-checking method, the faster and more intuitive it will become.