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

Example 2 – GCF of 48 and 60 Using Shared Ladder

Divide both numbers by common primes simultaneously. Stop when they share no more common prime divisors.

GCF(48, 60)

Both even → ÷2: 24, 30. Both even → ÷2: 12, 15. Not both even. Both divisible by 3? 12÷3=4; 15÷3=5. Yes → ÷3: 4, 5. No common prime factor left.

GCF = 2 × 2 × 3 = 12. LCM = 12 × 4 × 5 = 240.

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