What is a division ladder?

Answer 1

A division ladder is a method of finding the prime factors of a number. The number is divided by a Prime number. That result is divided by another prime number. This continues until the result itself is a prime number. This result and the divisor from each step are the prime factors of the number.

Here are the steps, but not quite the appearance of the division ladder.

108

÷ 2 = 54

÷ 2 = 27

÷ 3 = 9

÷ 3 = 3

The prime factors of 108 are 2, 2, 3, 3, and 3.

Here is an example that better replicates the appearance of a division ladder that goes downward.

2 | 168

...-----

..2 | 84

.....----

..2 | 42

.....----

..3 | 21

.....----

.........7

The prime factors of 168 are 2, 2, 2, 3, and 7.