Factors, Multiples & Primes
Ladder Method – Prime Factorization by Repeated Division
The ladder method (also called the division ladder or upside-down division) is a systematic way to find prime factorization. Instead of branching outward like a tree, it stacks divisions downward — making it easy to see and tidy to write.
Because the ladder method stacks numbers in tidy columns rather than spreading outward like a tree, it scales especially well: the same technique extends naturally to three, four, or more numbers dividing down a shared ladder at once, something a factor tree cannot easily do. This makes it the method of choice whenever you need the GCF or LCM of an entire group of numbers together, rather than just a pair.
How the Ladder Method Works
- Write the number inside a partial box (the “ladder rungs”).
- Divide by the smallest prime that goes in: 2, then 3, then 5, then 7...
- Write the quotient below.
- Repeat until the quotient is 1 (or a prime for single-number use).
- The primes on the left are the prime factorization.
Example 1 – Prime Factorization of 72
72 ÷ 2 = 36 | 36 ÷ 2 = 18 | 18 ÷ 2 = 9 | 9 ÷ 3 = 3 | 3 is prime. Primes: 2, 2, 2, 3, 3 → 72 = 2³ × 3²
Ladder vs Tree – Comparison
| Feature | Factor Tree | Ladder Method |
|---|---|---|
| Layout | Branches outward | Stacks downward |
| Best for | Visual learners | Systematic/written work |
| GCF/LCM together | Harder | Easier with shared ladder |
| Large numbers | Tree gets unwieldy | Clean column layout |
Key Takeaways
- Always divide by the smallest prime possible at each step.
- The ladder method keeps work organised in a column.
- Using a shared ladder lets you find GCF and LCM in one process.
- Both tree and ladder give identical prime factorizations.
Practice: Ladder Method
Ladder Method Question