Finding Common Factors

Number Theory · Axiom Academy

Discover how numbers share divisors through real-world packing, tiling, and grouping problems. You have 12 apples and 18 oranges. You want to pack them into identical bags where each bag has the same number of apples AND the same number of oranges. Try different bag sizes! You want to tile a rectangular floor that is 24 units wide and 36 units long using square tiles. What tile sizes will fit perfectly with no cutting? Let's explore the factors of two numbers and see which ones they share. Click the numbers below to see their factors! Find the Greatest Common Factor Now you try! Adjust the sliders to pick two numbers, then find their Greatest Common Factor. When dividing items into equal groups (teams, bags, boxes), common factors tell you the possible group sizes that work for ALL items. In tiling, cutting boards, or any construction project, common factors determine what sizes fit perfectly without waste or cutting. The GCF lets you reduce fractions to their simplest form. For example, 24/36 simplifies by dividing both by their GCF of 12 to get 2/3! Common factors help solve problems about repeating events - like when two different cycles sync up or how to schedule recurring activities.

This is the written version of the interactive lesson above. See the full Number Theory course.